A 30A service would need running 3600W. Also keep in mind, pretty much any 30A trailer with an AC AND a Microwave can be overloaded and throw the breaker. A 50A (and 240V) service can use up to 12000W total. That is a MASSIVE portable (and RV) generator and not practical to be moving around as you camp/travel. So you will have to make a compromise on what you use in the trailer while on generator and get one that makes sense.
As noted, you need to figure out what size makes sense for your needs - look at the big items (battery converter, fridge, each AC unit, furnace) and figure out what their power draws and what your likely needs will be. Pro-tip, you won't need furnace and AC at same time so keep that in mind when doing your math.
Something else to explore if you want to do off-the-grid camping: buying a bank of high quality deep-cycle batteries and an inverter and a transfer switch. You can use the batteries and inverter to power the trailer and only run the generator for a few hours a day to charge the batteries back up.
I got this generator for my trailer (only a 30 Amp) and have been very happy with it so far. It is an inverter generator but open frame so slightly louder than other inverters. Due to this though, it is very low cost for the output that you get. It is about 100 pounds, so hoistable into a truck and back down if you are spry (and maybe at the younger end of the spectrum - I am only 31).
https://www.amazon.com/gp/product/B01M3R711N/