Firstly the most important factor when it comes to choosing a dive computer is the colour and the size of the computer as everyone knows that Scuba Divers are a vein lot and like to show off with big watches and brightly coloured gear - JUST JOKING - (divers have a sense of humour too!)
Right onto the real factors.
You must firstly decide whether you want a console mounted computer or a wrist mounted Dive Computer. Some Dive Computers come with a wrist band but can actually be taken out of the wrist band and placed into a console so you can change the arrangement at a later date, however many computers don't so you have to make the decision when you purchase the computer.
So let's run through some pros and cons of a wrist mounted Dive Computer.
It is a personal choice and can often be decided by what you are used to using as a recreational diver if you are hiring equipment you will most likely get used to the set up and configuration of the hire equipment and therefore will tend to make your decision based on that. However I strongly urge you to consider what type of diving you plan on doing before making your choice. What I mean by that is are you going to remain a pleasure dive taking easy fun dives just for leisure or do you plan on becoming a dive professional or a technical diver? Depending on that type of diving you plan on doing should help you decide on what type of Dive Computer you will choose.
Will you need a Nitrox Dive Computer or an Air Dive Computer?
Will you need an Air Integrated Dive Computer?
Will you wear your Dive Computer on your wrist or in your console?
As a Dive Professional I personally prefer a wrist mounted computer as I generally need my hands to be free to assist student divers. In the case that I have a diver panic I need to be able to control that diver and obviously help control their assent if they are trying to make their way to the surface. By have a wrist mounted computer I can hold onto the student and keep my computer at eye level to ensure we are not making a rapid ascent, where as if I had a console mounted computer on hand would be tied up holding my console up to eye level.
If you plan on doing technical or deep diving that will require deco stops or if you find yourself in tight crevaces, caves or swim throughs I personally think it better to have a wrist mounted computer. Again for the fact that while you are holding you deco line you have you Dive Computer at eye level so it just takes a glance to check your depth and time rather than having to hold the deco line and the console. Also while in tight areas you may not be able to reach your console where as a wrist mounted computer will be at hand always.
If you don't plan on becoming a Dive Professional or a Technical Diver then a console mounted Dive Computer may be a better choice. Generally in pleasant recreational diving your dive computer is merely going to be used as a timing device to work out your tables to keep you safe from staying down too long, you are not going to need to continually check your computer while making rapid ascents or at great depths. For this reason it is in your console, out of your way and is there for you to check on it every so often during your dive just as you do your air. The other advantage of having a computer on your console is that it will always be a part of your dive gear so when you pack for a dive you know that if you have your regulator set up in your dive bag then your computer is there too unlike a wrist mounted computer which could be easily left at home when you go diving. So again for recreational purposes a console mounted diver computer make a lot of sense.
Also as you most likely won't be handling panicked divers or decompression stops you will not need to monitor your dive computer on every ascent as you become used to making a slow ascent yourself.
These are the 2 main factors you need to consider. However as I mentioned before you must plan for the future and take into consideration if you plan on diving with Nitrox then you will need a Nitrox compatible computer to keep you safe on your dives.
You can also get air integrated dive computers that will keep track of your air as well as your depth and times so doing away with one extra Dive Gauge on your console. You would chose a computer like this if you want to stream line your dive equipment and you are comfortable with using computer based technology to monitor your air supply while on a dive.
If you are really interested in streamlining your Dive Equipment then you can get air integrated hoseless wrist mounted Dive Computers which have a transmitter attached to your first stage regulator instead of a hose allowing you do away with any Dive Gauge Console completely. Again you must be comfortable using technology to monitor your air supply - this time without a hose. These computers are a great way of streamlining your equipment as we all know how bulky your dive gear can be.