The techniques for various types of astrophotography are different so there is no single answer.
- Planetary Imaging typically involves a telescope with a long focal length and a very fast camera that captures video frames at a high rate. Guiding is not needed. The data is captured within a few minutes. Processing this data is also very different.
- Deep sky objects (not in our solar system) such as nebulae, galaxies, globular clusters, etc. involve larger sensor cameras which take long exposures (e.g. 5 minutes) and the better versions of these cameras have cooled sensors to reduce noise from heat. The focal length needed varies based on the target. Guiding usually is needed except for short focal length (wide field) objects (e.g. focal lengths around 500mm usually don't require guiding.). Data is typically captured over a period of hours. Field rotation will be a problem with alt/az type telescope but not with equatorial telescopes. Consequently, equatorial scopes are highly preferred, but the largest telescopes on the planet are alt/az and use a field-rotators to compensate.
- Solar (and sometimes Lunar) imaging typically leverages narrowband telescopes (e.g. Hydrogen alpha wavelength solar telescopes) and high-speed cameras (preferably with a global shutter).
- Nightscape photography (e.g. Milky Way photos over a landscape) do best with cameras that have physically large sensors (e.g. full-frame sensors) and usually a wide-angle lens and tripod. This type of photography typically involves the least specialty equipment although a tracking head is helpful.
- There is a middle-ground which uses moderate focal length camera lenses (no telescope) to take a region of sky (no landscape). The only special equipment needed for this is a tracking head for the photo tripod.
I left out comet photography because you specifically mentioned that topic ... so I'll address that with a bit more detail. But mostly I mentioned the above points to make it clear that there's no single set of gear that lets you do everything -- and no "best" set of gear. Most astrophotographers end up owning a variety of equipment and select the equipment based on the target.
For most types of astrophotography, light pollution is your enemy -- and you seek dark skies on moonless nights. Planetary photography is a bit of an exception because most popular planet targets are bright enough that light pollution isn't much of a problem.
C/2020 F3 (NEOWISE) is currently headed away from the Sun. This means the amount of off-gassing is reducing. Most of my astronomer friends say it is no longer a "naked eye" comet (at least not from moderately light polluted skies). Some type of optical aid is needed.
The moon is currently waxing (1st Qtr will be Monday July 27, 2020) and it will continue to brighten until it reaches full moon. Remember light pollution is your enemy. The main point here is... you don't have much time left to capture the comet.
All astrophotography involves at least two main phases... image data acquisition, and image processing. Both can be somewhat complex (astrophotography has a reputation for being one of the most technically complex types of photography). Many astrophotographers that I know will tend to discourage astronomy novices from attempting astrophotography because it can be very frustrating. Attempting to learn the sky, learn to use telescopes, telescope mounts, etc. and then attempting to learn astrophotography data acquisition techniques and processing techniques all at the same time can be a bit overwhelming (consider yourself warned). Also, many types of astrophotography can be quite expensive.
A decent photo tripod is essential because you will be taking multi-second exposures.
For most types of astrophotography, you have to contend with the rotation speed of the Earth. The planet rotates at a rate of approximately 15 arc-seconds (angular rotation) per second. In a 4-second exposure, an object will have moved by 1 arc-minute. In a 240 second exposure (4 minutes), an object will have shifted in the sky by 1°. This effect can be cancelled with a "tracking" mount.
An equatorially aligned tracking mount means that a motor is rotating the mount at the same 15 arc-second per second rate. If the rotation axis of that motor is parallel to Earth's axis (it is polar-aligned) and rotating in the opposite direction, then that rotation will cancel the Earth's rotation and the camera will remain pointed at the same section of sky (even for hours).
Whether or not the sky moves enough for a non-tracking camera to notice the motion depends on the image scale (the angular field of view of the sky per pixel).
There are numerous image-scale calculators available on the internet, such as this one: https://astronomy.tools/calculators/ccd
But the short version is... the wider the field of view, the less likely you are to notice the movement and the longer you can expose the image before you end up with elongated stars that have "trails" behind them instead of pinpoint stars. If you have a camera mounted to a polar-aligned tracking head then this issue is moot.
Image acquisition the easy, but more expensive way
Acquire a tracking head. I use a Losmandy StarLapse head (http://www.losmandy.com/starlapse.html) but it is no longer manufactured. It is SOLID (30 lb payload).
The popular tracking heads these days are the Sky-Watcher "Star Adventurer" and the iOptron "Sky Guider Pro". Both vendors (Sky-Watcher and iOptron) make two tracking heads... both have a 2.5kg (5.5lb) version and a 5kg (11lb) version. Don't waste your time with the 2.5kg version ... if there's one thing I've learned in my years of doing astrophotography is that you want the beefiest equipment you can manage. If the beast is so heavy that it requires a visit to your chiropractor the following day... that's the one you want!!!
They also offer some solid tripods if you don't already own a beefy tripod (remember... you want something back-breakingly heavy... if it's light, it's going to flex & shake during your long exposures).
Having this, you can "polar align" the mount (which means the rotation axis is parallel to Earth's rotation axis ... they usually include some type of alignment aid to help you get it precisely aligned), you can attach a camera and start imaging.
The lens of choice depends on the field of view needed for the comet and it's tail. C/2020 F3 NEOWISE has a tail roughly 5° long ... using a camera with an APS-C sized sensor (most DSLRs), a 200mm focal length would work quite nicely. This isn't a "rule" ... just a something to think about when selecting your lens.
If you are on a tracking head, you can expose as long needed. This means there is no need for high ISO. I'll provide a sample image of my own. But better advice is to use a website such as AstroBin. AstroBin is similar to many photo-sharing sites except it specializes in astrophotography images. More important ... most photographers share their exposure settings! This means you can sift through images to find photographers using equipment similar to what you have available and see what settings they used.
You will always only ever use manual exposure settings in astrophotography. This is because auto-metering systems won't be able to reliably predict the exposure for a night sky.
You will always only ever capture images in RAW mode (never JPEG). This is because JPEGs do not have enough adjustment latitude to survive the post-processing steps required.
When I captured NEOWISE, I used a Canon 60Da camera (this is an APS-C DSLR but the "a" suffix is because this is a special-edition created for astrophotography. The internal filter is replaced with a filter that allows more of the visible spectrum to pass through to the camera's sensor. Most cameras use algorithms that try to match the sensitivity of the human eye ... astrophotography cameras try to capture as many photons as possible and do not try to mimic the response of the human eye.)
I used a 200mm lens at ISO 800, f/2.8, and took a 5-minute exposure on an aligned tracking mount.
Focus must also be performed manually. Working in your favor is that fact that if anything in space is accurately focused, then everything in space is in focus (it's all the same focus distance).
Start by finding the brightest star you can identify in the sky (do not use a planet... it must be a star because you need a true "point source" of light and a planet is a disk, not a point.
Switch OFF autofocus and image stabilization features.
Manually adjust focus to the infinity point.
I use the live-view feature on my camera and my camera (but not all cameras) have an "exposure simulation in live-view" mode. This means the view gets brighter if you crank the ISO to max, set the f-stop to wide-open, and set the exposure time to 30-seconds (or the longest duration your camera can handle).
- Zoom the live-view on the star and carefully adjust focus to make the star as small as possible.
If you can, use a Bahtinov focus mask. I use one of these:
Having refined your manual focus, return your exposure settings to sane values, remove the focus mask, and point the camera back at the comet. Start the tracking head and make sure it is tracking at sidereal rate (the speed that the stars move).
Here's my shot ... I used 5-minutes (this is a single shot only ... not a 'stack'). This only works because the camera is on a tracking head.
Image acquisition the more complicated but less costly way
If you don't have a tracking head (and really...they do make life easier) you can still capture the comet on a stationary photo tripod.
You'll need to use the "600 rule" (or "500 rule" if you want to be more conservative). This suggests that if you were to use a "full frame" camera (crop-factor is 1.0) then you can divide 600 by the focal length of your lens. The result is the number of seconds you can expose without noticing the star trails. This doesn't mean there won't be star trails... it means if you don't pixel-peep, you probably will find it an acceptable image. (If you want to pixel-peep... get a tracking head.)
With a "full frame" sensor camera (36mm x 24mm) the crop-factor is 1.0. But these tend to be expensive camera bodies. More typical is the APS-C size (about 22.5 x 15mm ... but it varies a tiny bit depending on camera model). Those cameras have a crop-factor of 1.5x.
To compensate for any smaller sensor, divide 600 by the crop-factor. E.g. 600 ÷ 1.5 = 400. Now divide that result (400) by your camera's focal length and you get 2 ... a 2 second exposure. That's quite a reduction from the 5-minute exposure I captured above! And this creates a new problem... a poor signal-to-noise ratio (SNR).
Noise is the result of under-exposure ... all exposures have noise, but you mostly only notice the noise is an underexposed shot because the data has to be amplified (gain)... and amplifying the data amplifies everything the signal ... or data you do want, the noise ... the stuff you don't want.
At a 2-second exposure, you'll probably need to crank up the ISO (gain) and you want the fastest lens (read: most expensive) you can get your hands on. If you can find a 200mm f/2... that's the one you want. It's a bit easier to find a 200mm f/2.8 but even those aren't particular cheap.
Many cameras include a couple of entry-level lenses. Those lenses are designed to be affordable... so that a camera body and a couple of lenses. Those lenses will really be challenging to use because they are at f/5.6 when zoomed out to 200mm focal length (capturing only 1/4 the number of photons per second).
To compensate for this, you acquire more data samples... you set up the camera and start capturing 2-second exposures... for a very long time. You want hundreds of exposures. Since the Earth is moving, each frame captures a slightly different piece of sky and the comet will eventually drift out of the frame. So every few minutes you'll need to nudge the mount to re-center the comet.
These exposures will be "stacked" via image stacking software (post-processing). The software alignment process will match the star field in each frame to create a combined image.
But there's a new problem... (and remember, I did say this method, while cheaper, is more complicated... I wasn't kidding about the complicated part)... the amount of time needed to capture all these images means the comet will have moved in the sky by a noticeable amount.
The best software I know of for dealing with this aspect is PixInsight. PixInsight can do alignment based on stars (like most stacking astrophotography stacking software) but it has a special feature for comets. It requires that each image have it's date/time metadata attached. You stack the frames. You identify both the first frame and the last frame. Also identify the comet in the frame. It uses the comets position in each frame and also the time of the first and last frame to determine how fast the comet is moving. It then uses the time for each unique frame to nudge that frame so that the comet will align (instead of the stars). You end up with a result where you have a sharp comet and sharp stars. But PixInsight has a bit of a learning curve and it is moderately expensive (I think it is €230).
I only really covered image acquisition... and only for comets... and you can see that was a fairly lengthy post (astrophotography is complicated).
I'm not going to cover post processing methods (other than mentioning image-stacking).
Post processing is needed because most objects in deep-space tend to be very dim. You wouldn't like the straight-out-of-the-cameras photos (with few exceptions) and require some stretching of the data to tease out the details (basically you're trying to make things that are faint, subtle, and very difficult to see... very bright, obvious, and easy-to-see.