Sounds very doable with a modest gas powered generator within your budget. Shop around and watch for sales.

Also, I should have mentioned, consider the size of the gas tank on the generator. Smaller generators have smaller gas tanks that may require refilling every couple of hours. You had a 26 hour outtage; how would it be to refill it 10 to 12 times? Consider models with a 5 gallon tank that will run maybe 8 or more hours on a tank.