What are the most important factors that need to be kept in mind while purchasing a manual flash gun?
To me, a "manual flash" means a simple non-TTL flash. When shopping for those, the five essential things to look at:
There are some other optional features that may or may not be important for you:
By saying "manual flash gun" I assume you mean a speedlite kind of electronic flash with manual controls. Modern flash units pack a lot of goodies and provide excellent chance for customizing your lighting setup. I am familiar with the Canon lineup so the examples below are of Canon flashes but they apply to other brands as well.
The first factor to consider, would be the flash's power (measured in Guide Numbers). For a hobbyist use, most of the time you don't need the most powerful units. This means that, depending on your typical shooting conditions, you don't necessarily need a 580EXII but can easily do with 430EXII (I do not mention the other, cheaper ones, b/c you asked about a manual unit). Anyway, the more power levels you can set in your flash, the more flexible you will be with setting up your shoots. Going from full to 1/128 can be useful sometimes but most of the time you don't go that low in the output settings. But, have at least 4 steps of settable power, which make a difference between full lighting of the subject and some strong fill-lighting. For more delicate work you will want finer control.
Then come the other set of features. Manual flashes tend to have a zoom setting as well. This will let you control the spread of the beam. It is one thing lighting one person for a portrait work and a different thing lighting a group. Some units also offer additional diffuser to spread the beam even further at the min zoom settings.
If you shoot a lot of on-camera Speedlite photos then E-TTL (I-TTL for Nikon) is invaluable. It means that the flash exposure is determined by the exposure metering of the camera and you can shoot automatically.
Tilt and swivel are almost always very handy as it lets you avoid direct flash lighting of your subject. This will let you aim the flash at the ceiling/wall to have a relatively huge light source, casting very soft and flattering light.
For some types of photography, like daylight and action shoots the High Sync Speed feature is important. It will let you fire the flash when the shutter speed is faster than the Sync Speed (usually 1/200-1/250 sec). This is crucial for freezing fast moving subjects.
If you are doing off-camera lighting then you can fire the flash with a cable or some (optical or radio) slave. Canon and Nikon have integrated wireless control where your built-in flash or an external transmitter/speedlite serves as the commander to control the setup and firing of the slave unit. A combination of wireless and TTL is awesome. If your camera doesn't have this functionality then virtually any flash/camera can be paired with a cable but there is no TTL in this case. Radio control will let you put the flash in a softbox, where there is no Line of Sight for optical slaves.
Another factor is the weight. Pro units become very hefty. If you own a small camera then a pro unit will make the combination look pretty weird, and more important will introduce some imbalance in the whole setup. My Canon S5-IS P&S equipped with my 580EXII flash really look like a flash with a camera mounted at the bottom... For extended shooting sessions you will feel the hand fatigue holding and balancing the big load.
Lower in importance are factors like integrated bounce card (easily added by a rubber band and a piece of white paper). External power connector may be important if you shoot very fast or for extended sessions. AFAIK, only pro units offer these power packs.
Syl Arena's Speedliting.com has some good information on the techniques and equipment for flash photography (Canon-centric, though, but applies for other brands as well).
A few quick thoughts
It's first on the list because if you can't afford it, well: you can't afford it ;)
How much light does it put out?
It's worth hitting the reviews for this one, but in this day and age, your strobe should trigger every single time without fail.
If you're shooting slowly this won't be so important.
I can't think of the right term here (edit, someone? anyone? Bueller?), but how many stops can you turn the power down? Also, does it turn down in full stops? half stops? thirds of stops?
How do you get it to flash?
Will it fall apart the first time you drop it a couple of feet?
weight / size
You're presumably plannig to hump this around.
Does it have a way to easily attach colour correction gels?
If you're purchasing a new manual hotshoe flash that you will, presumably, be using off-camera Strobist-style, I'd look at and for the following features:
The guide number is (sometimes) a good guide for this, but make sure you know the ISO setting and zoom settings that were used to measure the guide number. For some third party units (e.g., Yongnuo), the guide number in the spec can be considerably higher than how the flash tests out. It can often be problematic to determine just how powerful a flash is, and comparing guide numbers of different models may not be always be comparing apples to apples. Also make sure you know what units the guide number is stated in (meters or feet). The higher the number, the higher the power output from the flash.
Also, be aware that there are some speedlight-sized bare bulb flashes out on the market now that are manual lights that can give you up to four times the power that a single speedlight can, with a more even light spread, more similar to a studio strobe than a hotshoe flash (e.g., the Godox Wistro).
Power Setting Range and Increments
Not all manual flashes have settings that go down to 1/128 power in 1/3EV increments. And lower power settings can come in mighty hand for macro shooting, like product or food shots. A Vivitar 285HV, for example, only has the 1, 1/2, 1/4, and 1/16 settings. Determine how much control and how wide a range of power settings you'll need for the work you want to do.
Tilt and Swivel
While you may not need this for bouncing, like you would on a TTL on-camera flash, it does still come in useful for off-camera work, if you're using optical slaving, so you can point the sensor towards the "master" flash signal.
Many 3rd party manual flashes include multiple features for syncing. These include the following things:
Dumb optical slaves can be very useful, as all it takes to set off the remote flash is another flash burst. It makes adding your flash to an existing light setup very simple, and you don't need additional gear (like a radio receiver). It is more line-of-sight and range limited than radio triggering, and can be set off early by pre-flashes in TTL setups; but some manual flashes also have slave modes that can ignore one or more preflashes.
The PC port (Prontor-Compur) is the traditional flash sync connector. You can get a PC cable to connect your camera to your flash and trip the flash remotely that way. Or you can use the PC connector to connect radio triggers.
The 3.5mm phone jack (or sometimes 2.5mm) on flashes is a much more recent development than PC ports, mostly introduced by Lumopro on their LP120 flash (although flash users had been modding flashes to add them for some time by then). The phone plug makes for a much more robust connection than a PC connector. It's also a much more commonly available connector, and given how many radio triggers also sport 3.5mm or 2.5mm phone jacks, this means you can purchase or make simple audio cables to use as sync cables.
Built-in radio receivers often have the downside of requiring that you buy same-brand transmitter units, but most of them do come with an upside: remote power control.
Remote Power Control
While a built-in receiver may only work with a transmitter from the same brand, the company that makes both the flash and the triggers can also build in manual power and/or zoom control. This happens with studio strobes as well (e.g., Paul Buff lights and the CyberCommander) and this is now happening with speedlights as well (e.g., Yongnuo YN-560III/IV with a YN-560-TX, Cactus V6 with the RF60, Godox V850 with FT-16S, etc.).
Remote power control, when doing off-camera work can become very handy, particularly if you're stuffing the flash into, say, a Westcott Apollo softbox and would like to avoid having to open up the softbox every time you want to adjust the flash's power output. Or you're putting your flash somewhere not easily accessible, like outside the window of the room you're shooting in, or high up in the bleachers for a basketball game.
Automatic Power Control
Some older manual flashes can't do TTL, but they do have a circuit to act as a sensor and auto cut-off switch for the flash pulse. In other words, Auto mode (or an autothryistor) is an older technology that was used to auto-set the flash power before TTL came along. This feature is mostly found on older vintage flashes than current new manual flashes, but if you plan on using the flash on-camera as well as off, it could be handy to have in run'n'gun event as an alternative to TTL. You will need to enter the ISO and aperture setting you're using into the flash.
Battery Port or Technology
A battery pack port can be useful if you want to avoid swapping batteries all the time, or wish to reduce the recycle time of the flash. But you can't use one if you can't hook one up to your speedlight.
In addition, there are now flashes coming onto the market (e.g., Godox V850) that don't use AAs, but rather proprietary Lithium-Ion packs that essentially replace an external battery pack.