Hiya Mate
I am a rescue technician and recovery trainer by trade and have 10 years experience in recovering vehicles from stupid places and watching idiots that don't have a clue trying to kill themselves. The choice of winch you want is primarily down to 3 factors.
1) cost. How much money do you want to spend? If you don't have a lot of money then you can get a cheap 12000lb rated electric winch off ebay for around £250-£300. A superwinch or warn winch and bumper kit will set you back about £600 from rebel 4x4. You can also get an ex utilities shaft driven superwinch off ebay complete with either drive dog or pto, bumper and drive shafts for about £250-£350.
2) Use. What do you want to use it for? If you are intending to use the winch all the time (competition type of use/frequency), want it to stop and start on the button without over run or want to use the full length of cable and reel it in in a non stop pull then stay away from electric unless its a Warn 8274 or you know your stuff with snatch blocks. If it is an occasional get you out the mud affair for when greenlaning electric is fine.
3) Competency. How competent are you at D.I.Y. and using a winch correctly? Hydraulic are the most reliable but if you buy a hydraulic winch can you fit it? and if it stops working, bursts a pipe or a spring goes inside the valve can you fix it? If you overload a shaft driven winch it is generally just a case of fitting a new cottle pin and carrying on. With electric winches its generally a case of new motor or solenoid.
Do you know how to properly use single, double and multiple line pulls to extract you from the deep stuff?
In short.
If you are a beginner with a winch then I would recommend that you get an electric winch to start with because you will hear the motor start to struggle before the cable snaps and so can stop and re-think the situation before the cable breaks and takes your head off. If you are a bit more advanced and want the control then I would go for shaft driven purely for control and multiple speed reasons (5 forward speeds and throttle control). If money is no object and you know how hydrualics work then hydraulic is the strongest.