I'm sick of the hassle of bottling, so I want to get a fridge and keg setup. Obviously it needs to be able to fit the kegs, but is there any other things I should look for in a fridge? I don't mind spending a bit more money, but I don't want to bring it home to find out it won't work with the other equipment.
In my opinion, not much at all. Make sure it seals OK, make sure it cools & make sure you have room for all the kegs you want to fit (many fridges have sloped bottoms).
I found a working but nasty-looking fridge to save cash, it lives out of sight but a lick of paint covered up any "beauty spots" it had. When I got it I cleaned the inside quite thouroughly - I don't think it matters to the sealed keg inside but nobody likes a fridge with gobs of old food stuck to it.
Once you've got the fridge, I recommend investing in a variable thermostat like this or this so you can use the fridge for fermentation as well as getting the perfect temperature for dispensing. If you're going to grab one of these, you can even put it in a freezer if you find a better size / fit / price.
A fridge is fine if you don't plan to use a temp controller with it. My first keg fridge was a normal standing fridge. Worked great. But now I use a small chest freezer with a temp controller.
If you were planning on using a temp controller then I'd go with a chest freezer. Its just a little neater with the lines running around. I find it easier to connect and disconnect the lines and play with releasing pressure when you have full access to the top of the kegs. IN a standing fridge I always found myself having to pull a get out to get to it. And the kegs in the back were always tough to get to. With a chest freezer you open the top and have full access to any single keg at a time. Much better IMO.
For fermenting, I use a 4.x cubit foot "dorm fridge" commonly used by college students or single-room apartment dwellers. No need to buy a new one, just keep your eye on Craigs List or your local equivalent. When a posting appears, take a look at the fridge and make sure you can slide in a carboy or fermenting bucket. Mine has a top "freezer" rack that only comes down a few inches and was used to make ice cubes I guess. I ignore it, but on some models, this freezer space will be too big, and you won't be able to slide the carboy in. Keep in mind that you can cut the shelves out of the door itself if needed.
For kegs, I'd go with a deep chest instead of a fridge. Again, look for used models first, but I ended up buying a new one that was slightly damaged from a big box retail place. You can totally trick out a chest freezer with tap handles and the like, if you are willing to build a wooden "collar" to go on top of the unit.
For a chest freezer, you must weigh the cost of the unit versus how many kegs it will hold. I can't recall the dimensions of mine exactly, but it holds 3 kegs, a 5lb tank, and a secondary fermenter or a No Chill tank just fine. This suits my needs perfectly, and I'm glad I didn't skimp and get a smaller one just to save $50-60. A good suggestion is to make a couple of disks out of cardboard that are the diameter of your kegs. Then, if you are looking at a chest freezer and aren't sure how many kegs it will hold, pull out the disks and position them around to figure out the freezers capacity.
Also, make sure the chest freezer is tall enough to fit kegs with an inch or two extra for the gas/liquid ins/outs. If its not tall enough, then you will have to build a collar, and that's kind of a pain.