So I have a Canon T3 and I wanted to take pictures of the night sky and landscapes but since I'm a noob at photography, I was wondering which lens should I invest in that isn't quite pricey. I was also wondering which mode and which setting should I set when I take pictures of the night sky.
I was wondering which lens should I invest in that isn't quite pricey.
Well, first off, lenses aren't investments. They're expenses. Nobody really buys a lens with the express intent of waiting for it to appreciate and then selling it at a profit. :) And "pricey" is in the eye of the beholder. I might tell you the EF-S 24mm f/2.8 STM pancake lens if you wanted a fast(ish) wide prime, or the EF-S 10-18 if you needed an ultrawide, but I'm not sure you're at the point where you'd know.
Quite honestly, if you don't know what lens you need, you're probably not ready to buy another lens just yet. The answer to what lens to get is a highly individual one with a lot of "it depends" factors, including what you want to shoot, how you want to shoot, your budget, and what gear you already own, and what's causing you the absolute most frustration.
For most folks just starting out with their first dSLR, for shooting landscapes and the night sky, you're probably best off sticking with the 18-55 kit lens that came with the camera. For landscapes, put your camera on a tripod, stop the lens down into the f/8-f/16 range, and amazing things can happen. The photographer who took that image did so with the six megapixel original Canon dRebel (300D) and the first version (non-IS, non-STM, softer optics) of the EF-S 18-55 kit lens. While nice lenses inevitably can help, mastering basic technique is liable to help you far more. And here's another photographer who shoots the stars and the Milky Way with am 18-55.
The most effective way to spend your money early on is probably on a book, class, or learning videos to get good basic technique under your belt. I'd recommend starting with Bryan Peterson's Understanding Exposure, but I'm a book learner and everybody is different.
I was also wondering which mode and which setting should I set when I take pictures of the night sky.
And this is why getting a book on exposure basics is a good way to go. :) You'll also want to look at the [astrophotography] tag here on photo.SE.
The answer depends on what you mean by night sky.
For photographing landscapes, stars as well as the blue hour the best start is actually a tripod and not a new lens. It allows for longer exposures in dark conditions. Additionally you can easily create landscape panoramas with the help of the tripod head.
From there use a lens whose focal length fits to the desired composition. Use aperture priority mode or manual mode and set the aperture to F8 - F11 (except for stars) and use a low ISO. For stars use the brightest aperture available and higher ISO. For wide landscape shots you can easily create a panorama using the tripod head.
If you want to photograph stars, the next step would be a wide lens (<=24 mm) with a bright maximum aperture (<= F2.8). Samyang has good manual focus+aperture offerings in this range.
The essential thing for night photography is a tripod. If you do not already have one, that is where you should spend your money. A cable-release helps too but I don't recall if your camera has one. Check the manual first.
Then you should get a good quality lens, preferable one with a bright aperture. The brightest, the more you will be able to see while framing. Although you would be mostly using Manual Focus, a bright lens is beneficial to autofocus too.
Canon has a 50mm F/1.2 which is very bright and excellent but I would consider it too tight for general landscape photography, so you will have to compromise and get something not quite as bright but wider. A Canon 24mm F/1.4 or the Sigma A 24mm F/1.4 DG HSM will both do very well. If you really want flexibility of zooming then you have to comprimse some more, although I highly recommend the Sigma A 18-35mm F/1.8 DC HSM which is a superb lens and currently the brightest zoom.
I was wondering which lens should I invest in that isn't quite pricey
Well lenses do not contribute to image quality in dark , it is the aperture and the shutter that control the amount of light entering the camera.
which mode and which setting should I set when I take pictures of the night sky.
There are 2 ways,
Use a larger aperture starting f1.5 and increase the ISO to about 6400. Click a shot to see if the you get a clear picture, if not just increase the ISO till you get a better picture.
Use a larger aperture starting f1.5 and decrease the shutter speed to 1s. Click a shot to see if you get a clear picture, if not just increase the shutter speed to 2s and so on till you get a better picture. Note: For this setup to work, you must use a tripod or else you might get a blurry image.Also it would be better if you press the shutter via the remote.