>Any recommendations on where to buy an affordable yet capable deep cycle battery?
Depends on your loads. Figure out how much each of your loads uses, multiply by the number of hours a day you will want to use it, add all of them together, and that will give you how many watt hours you need. For 100 watt-hours or less I'd go with one or two 7-10 amp hour gel cell alarm batteries. They are well sealed, easy to carry and readily available at hardware stores. USE FUSES! For a 150 watt inverter (should be all you need for the loads you describe) you're looking at a 15-20 amp fuse, or 2 10 amp fuses (one on each battery.) Connect fuses on the positive side.
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For bigger loads (up to 500 watt hours) I'd go with something like the Exide Orbital ORB34DC-36 deep cycle marine battery. More pricey ($200) but will last years, is maintenance free and is easy to lug - 40 pounds, no electrolyte to spill. Once again - USE A FUSE! If you short out a battery like this, the wire you short it with will become red-hot, burn through its insulation, burn through whatever it is resting on (your tent wall, plastic table, battery case etc) and then start a fire. All the while you will be standing there flapping your arms because the wire is now way too hot to touch and the connectors are burning your fingers. Don't ask me how I know this.
For an inverter, for SMALL loads you can go with a Radio Shack mod-sine inverter (the really cheap ones that plug into cigarette lighters.) They go up to about 150 watts. They sometimes create buzzing on radios but they're cheap. ($12!)
For larger loads I've had good luck with the Samlex true sine wave inverters. The PST- 30S is about $140 and is rated to 300 watts but will easily surge to 500 watts to start larger devices. They are also way quieter (electrically) than the cheapo Radio Shack inverters.
