chris, a little electricity 101 may help you (or it may just confuse you, in which case, sorry in advance).
Things that use electricity use it in watts. So if you look on the back of your TV and DVD player, you should find their usage rating in watts, or possibly in amps. Since watts are equal to voltage times amps, if your voltage is 120 VAC and you use 3 amps, you are also using 360 watts.
Wires carry electricity, but they are rated in amps. Any wire has a rating for the number of amps it can carry, and that is regardless of the voltage that is also being carried. So once you figure out the power you need, in watts, and you know the voltage you have, you will know the amps you need to carry and can look up the wire size. Remember - watts equals voltage times amps. Another way of saying that is amps equals watts divided by voltage.
Wire rating tables are all over the place. Some things that go into the rating are things like distance - the longer the distance, the bigger the wire has to be, the voltage drop over the distance, and the temperature rating. You have to know a bit to judge the wire size accurately, or you can just do what most of us do - ask Sean, or go one size higher as a comfort margin.
The size of your inverter is like the speed limit on a highway. You have an inverter rated at 600 watts, that's it's speed limit. You can go faster than the speed limit, for a little while, and your inverter can put out more than 600 watts for a few seconds - that's the surge capacity. If you speed too much, or take out too much power for too long, you get a ticket, or you blow a fuse, or your wiring gets too hot and so on - bad things happen. But your inverter is like your bus - it can go slower than the speed limit, or run at less than it's rated power output. So you could decide to run it at no more than 300 watts, put in a fuse and wiring rated for that, and away you go, happy as a clam. Just like you are in your bus at 50 mph on a 65 mph freeway, smiling at the birds and the cows on the side of the road...
So - what you do is decide how much power your TV and DVD player are going to use. I already looked that up and thought that 200 watts, including everything, was probably really close, but you can double check. For 200 watts at 12 volts, you have 200/12 = 16.6 amps. So you need a wire that can carry 16.6 amps for 10 feet, and I happen to know that 12 gauge wire will do that, I looked it up on a chart, and you could put in a 20 amp fuse. Or you could say that you have a big roll of 10 gauge wire handy, may as well use that. You look it up on a chart, or ask someone who knows, and find that 10 gauge wire will carry 30 amps at 12 volts, so you know that you can put in the 10 gauge wire, a 30 amp fuse, and have your inverter run up to 360 watts. Or you can say you want the full monte, your inverter is rated to 600 watts and 1000 watts surge, and you want it all, dammit! So you say, 1000 watts surge, that's 1000/12 = 83 amps, I have a 80 amp fuse handy, and I'll check on a chart, I need 4 gauge wire for that many amps.
So like many things in life, there are a lot of correct answers to your question, you just need to ask it right, and the right answer for what you really need to do pops out.
Hope this helped.
BTW, I do exactly the same thing as what you need to do in my bus, I run a TV and a DVD player off of a 750 watt inverter. I did the math, I said this sucks, I ain't buying 25 or 30 feet of 4 gauge wire, not this lad, and I put the inverter right beside the batteries (where it belongs anyway) and ran a little extension cord over to where the TV is. Remember the math - wire carries amps, and 750 watts at 120 volt ac is only 6.25 amps, and just about any little extension cord you can buy will carry that little amount of current.