We're all familiar with the kind of 12-volt batteries that start vehicles and are then charged by the alternator when the vehicle is running. These starting batteries are designed to deliver a lot of amps -- a very powerful current -- in a short time. Deep-cycle batteries can perform starting duties, too, but they're built with thicker plates that are designed to withstand numerous cycles of deep discharging and charging. They're more expensive than starting batteries, but, properly cared for, last for years of service.
Deep-cycle batteries like the one pictured here are available in three basic types -- flooded, gel-cell, and absorbed glass mat (AGM). Each type has its advantages, but for the simple purposes we're discussing here, we'd recommend plain old flooded-cell batteries. These are less expensive and more forgiving of charging foibles than the others kinds, and they work just as well -- again, given periodic inspection and maintenance. See 12-Volt DC Basics for a bit more information on amps and amp-hour ratings.
We hesitate to recommend an online purchase of deep-cycle 12-volt batteries, for a few reasons. First, they do have a shelf life. All else being equal, a battery that was manufactured six months ago will be healthier and last longer than one made 18 months ago. Second, shippers and handers have been known to leave shipments in freezing or very hot conditions for long periods before before delivery to the store. Third, the suckers are heavy and expensive to ship. Save the UPS guy's back and make sure you get a good battery by going to the store yourself.
Check the date of manufacture, check the battery's standing voltage, and if possible have the storekeeper apply a load test to it. If it passes with flying colors, as is likely, then all you have to do is check the condition of the cells once in a while (wearing eye protection), and add a bit of distilled water if necessary.
Deep-cycle batteries are available at all sorts of hardware and department stores, as well as places that supply RV-ers and boaters.