This page should give you the information you need to get your selection down to what will work best for you. The poor watt is often misunderstood. Watts are basically just a measure of how much power a device uses when turned on, or can supply. If a something uses 100 watts, that is simply the voltage times the amps . If it pulls 10 amps at 12 volts, or 1 amp at 120 volts, it is still 120 watts.
All wire has resistance, and amps flowing through a wire makes heat.
If your wire is too small for the amps, you get hot wires. This is not usually a good thing. AH are very important, as it is the main measure of battery capacity. Since most inverters run from batteries, the AH capacity determines how long you can run. See our battery page for much more detailed information.