Ha ha ha ha! Love it!
People typically start with something small, and then say, "Adding this would be cool!" And it is, if you can recharge the battery, like you can with the generator, it doesn't matter in the least
Some overkill of "the dreaded maths", as someone said in another thread:
I tested a 24 size Costco marine battery (85 Amp-hours x 12V ~= 1000 Watt-hours, of which about 600 Watt-hours are useable before the inverter screams) with a Xenix 4 channel mixer, 1000 Watt car stereo amplifier, powering two 120 Watt max living room sized Kenwood speakers by running them LOUDLY at home for like 10 hours a day a couple years ago. The battery lasted almost a full month before needing to be recharged.
Say your stereo takes 20 Watts normally (it's really lower), times 14 hours a day = 280 Watt-hours per day.
A big PC fan is under 8 Watts. Let's say you run it 12 hours a day. That's about 100 Watt-hours per day.
A 20 Watt light times 8 hours per night = 160 Watt-hours per night.
70 LED Christmas light strings are like 20 feet and use 5 Watts each. Using 8 of them for 160 feet times 8 hours a night = 320 Watt-hours per night. This is gonna be very, very bright! Cool!
This sums up to 860 Watt-hours per 24 hours. Add in another 15% due to inverter power loss, and say 1000 Watt-hours per day. It's really way lower though, especially so if some stuff is turned off at 1 or 2am, or if you only get 3 or 4 strings of the LED Christmas lights, which is enough to go around the car port.
So, for this, even for the full 100 Watt-hours per day, get a Costco size 27 (105 Amp-hour = 1260 Watt hour, ~700 W-h useable) or Malmart size 29 (114 Amp-hour = 1400 Watt-hour, ~800 W-h useable) 12V marine battery. And,you'll probably need like a 20 Amp battery charger, rather than the cheaper 10 Amp battery chargers. Still under $120 or so. And, turn on the generator for about 3 or 4 hours total daily, like early each evening or whenever. Protect both the car-battery-charger and the inverter from significant playa dust, both short out easily. That would handle it.
setup: generator -> car-battery-charger -> battery -> 12V PC fan and inverter -> stereo/disco-light/LED-light-strings
One trick is to just "wingnut down" the inverter "ring terminals" on the battery small posts, never removing them, this guarantees the inverter never sees more than the battery 12V or 13V during the week. Then "clip" the car-battery-charger to the bigger battery posts when recharging the battery. I think that most newer, better battery chargers can be left connected at all times also, others know better than me, or check the manual.
LED light strings, cool! Have fun!