Years ago I did a DIY battery backup using a car battery, car charger, Bosch relay, boat saltwater safe bilge pump & some wiring. The relay is wired to plug into the wall & when the wall outlet looses power it turns on the bilge pump. You can then determine how long you want to keep the bilge pump running & buy the proper size battery(s) from there.
I have a similiar set up for a back up home sump pump... you can get a similar watch dog kit for around $200.
Also I am wondering if you could have the pump/life systems turn on and off intermitently to extend your battery life even further... I think 10-20 mins off every now and then shouldn't hurt anything...?
Why not a generator, after that "hurricane" wind came through here, you can get em pretty cheap on CL, though they are slowly dwindling down now.
I always used my truck to power different items in a long power outage, I would park it in my garage and just run a cable into the house from it, and power on the lights, tv, comp, watersoftner etc...