You need 12 volts. The size of the battery (amp/hour rating) will determine how long you can run off just the battery.
I agree, gel-cell would be the ideal choice. Marine deep cycle would work, but I'd much rather use a gel-cell inside a house.
Depending on how long you want the radio to run off of the battery, and how much transmitting you will be doing, will dictate what size battery you need.
As KB2ZTX said, used Telecom batteries are idea. I'm a telecommunications engineer by trade, and work with radios and a very large PBX system. Our PBX is distributed over a wide geographical area, with some sites bigger than others. Our big sites have 1000AH and up battery plants, while some of the smaller ones might be 100AH. We usually retire our batteries before they fail, so they always have a few years of life left on them. We often donate them to local hams. Good places to check for used batteries would be any telecom installer that does small to mid sized systems. Since these systems usually run off 48 volts DC, it's pretty common to have a string of four 12 volt gel-cells providing battery backup. They should be replacing them -before- they fail. Another option is the batteries out of most home/office UPS systems. They usually use 12 volt gel cells.
A new battery is going to cost you some money. We use a lot of C&D Technologies model Tel 12-105's. These are 12 volt 100aH batteries that are designed to sit 4 across in a 23 inch equipment rack. They would be ideal for this application. Figure on paying somewhere between $230 to $250 each, new. Or, if you were local, I'd give you some for free.
While a gel-cell shouldn't outgas if charged correctly and not mistreated, they can vent hydrogen gas in certain instances. Do not put them in a sealed container. Make sure you vent them somewhere safe (outside). They can be installed indoors, without venting, but make sure you don't charge them with too much current or run a charger at more than 13.6 to 13.7 volts. Obviously, fuse everything.
As for chargers, you can full time charge them if you do it correctly. It referred to "float" charging in the telecom industry. You feed them with 13.5 to 13.6volt (or whatever the manufacturer recommends) and keep the current low. This will not overcharge the battery, and as long as the battery temperature stays stable (70's or so) you'll be OK. To do it right, you should have a charger that will do temperature compensation.
Sorry, probably way more info that you wanted....