The 3,000 won't do anything but yawn at a 5,000 BTU window A/C and say a 18 CF refrigerator.
Buy some rechargeable lanterns while you're at it. For use when refueling. Please be paranoid when refueling a warm, (but shut off) generator. I have become an unwilling expert in dealing with outages. Fans, really help.
General note: Sleeping when it's miserably hot and humid...
A tightly stretched out huge hammock. No blanket - not even a sheet. A blanket size swath of cheesecloth. Same for a pillow. Roll the cheesecloth up and stuff it under your head - it breathes. This is where a Fantastic Fan Endless Breeze will earn it's keep. If a mosquito tent is used, put the fan inside the mosquito tent. The tent blocks about 70% of an exterior fan's effectiveness.
Rubber boots, nitrile gloves, and a CO detector are to me, vital for working around a generator. A wind shift can poison a house and a CO alarm can save your life.