Always glad to see another woman going down the road.
Unless you're doing lots of boondocking you may not need a generator. Your battery will allow you to use lights for 2-5 days, if you are conservative. Your water pump will also wear out your battery. Driving your car does a minor job of recharging your battery, but hooking up to a 30 amp circuit will recharge it quickly. (HINT: If you're boondocking, UNPLUG the electrical connection from your truck, because the trailer will drain the truck's battery after it flatlines the trailer's!
What generator you choose depends on what you expect to run. If you're planning on having Air Conditioning you'll need a bigger genset. Many folks link 2 Honda EU2000's in series or get an EU3000 - which weighs about 140 lbs!. If you just want to run lights and fans a Honda EU 1000 which weighs only 37 lbs will do the job. I don't carry spare gas, I just siphon from the truck's tank. Use your SEARCH tool - there are also quite a few threads on propane generators.
Read lots here, you'll get tons of good ideas and attend at least ONE WBCCI rally! If you can find an "Airstream Only" park nearby, a long weekend practice run there would be in order. You'll get tons of advice and help just by asking.
Practice backing until you get it right. Your short unit will be squirrely! Less is more, a little bit is more than enough. The worst thing that can happen is that you get stuck in an area where you MUST turn, but can't master it easily. I'm not going to call myself a master, but I have gotten better - find a vacant parking lot and practice, practice, practice. Remember hands at the bottom of the steering wheel, move hands in direction you want the wheels of the trailer to turn. Whenever possible backup turning the trailer to your left - it's far easier to see where the trailer is going out of the driver's rear view mirror.
READ all that stuff in the big canvas case Airstream includes in the new units, it's all useful.