My son has a small trailer, and for the usage you're describing, you could use the same generator. A Honda 2000is (inverter) is a great little generator. It will meet all your current needs and more. It is one of the quietest out there. Personally, I have a 3000is, but unless I'm running the A/C I don't need that much power.
If you buy a 2000 watt Honda, and you need more power later in your camping career, you can purchase another 2000, along with a parallel kit. This will allow you to have 4000 watts and run most anything.