cheapest deep cycle batteries in UK are Deta Orbital from http://www.rthursby.co.uk/acatalog/deep_cycle.html IMHO, if the computer reboots during crank then use a tank circuit (search this forum) and if you plan to use the carputer for long periods of time without the engine running then use a split charge system and have a second battery so you can at least start your car when the main one dies.
if you can't find time to do it right, when are you gonna find time to do it over.
Popping in to recommend the Optima Yellow Top deep-cycle batteries. I have one as my car's starter battery and two for the auxilary battery bank system. Recharged via the car's alternator.
Good grief you're running three batteries? Why? What kind of systems do you have hooked up that you need three batteries? Outside of just preference I've only seen a few cars that had added electrical components that needed two batteries. I'm interested to know what you have in your ride and why you didn't just upgrade your altenator before buying three batteries.
To answer the original question deep cycle batteries are usually used for running electrical systems when a generator(altenator) isn't present. Basically meaning there mainly used for running electrical components with the car off. As stated above they're designed to run to a low charge and then can be charged back up without loss in performance. In most cases you usually would use the deep cycle as your second battery. Personally I'd say if you're only running one battery go with a optima red top starter battery, if you want to run two batteries go with whatever you're using now for starting the car and run the carputer off the optima yellow top.
Power drills and table saws. Seriously speaking, the aux bank is primarily used (other than block parties) for camping which requires long extended times between recharges. It has nothing to do with the output of the alternator or anything. I use the aux bank for other things other than the CarPC. There's a Xantrex XPower 1750 Plus inverter hooked up to it.
What everyone recommended above is a good place to start. I guess the next question is how often you're going to run equipment when the vehicle is NOT moving (i.e. not charging your starter battery). Second question is, what kind of CarPC you're wanting to install to figure out power requirements. Once you've figured that out, you can see whether if you just need a new starter battery or want to setup an aux battery just for the CarPC.