Google for off grid homes. If you have your battery and invertor rack in your living quarters, you stand the chance of a explosion from off gassing when the batteries are charging. Wet batteries give the best charge and discharge curves but they required more attention and there's the off gassing.
Lead acid GEL type batteries are a better choice. But if you run them down too far the amperage capacity is reduced.
Li ion is out because of the cost per watt. Extreme fire hazard.
LIPo are the same besides the fact the charging and discharging is so finicky you could blow yourself up and burn your house down.
Think of what you would want to operate when the power goes off and go from there. Anything you can convert to gas you should. Gas is cheap and is not dependent on the power being on. Gas heat, gas stove, and there's even gas fridges. Your gas heat needs to be radiant and work with out a blower. A free standing space heater depending on it's output, will warm several rooms. The loo is always going to be the coldest room in the house. Don't ask me why, just seems that way. You can install a small heater in there if you can afford it.
Switch to LED lighting. I get 20" long LED strips with 30 really bright 5050 smd LEDs on them. They run off 12 volts and pull very little amps. The strips can be chopped up and put under cabinets in the kitchen and tacked to the ceiling in other rooms. 20usd from www.superbrightleds.com
You can cut the strips up and make desk lamps and wall sconces. Let me add the strips are rigid not a limp noodle type that comes on a roll.
There's a lot you can do to add battery back up to those also. Just a 14ah gel battery with a float charger will let you have light from just one these strips for a couple of days run time if used sparingly.
How far you want to go depends on how much you want to spend to start off. It wil take a while to recoup the cost of hardware. I love LEDs. I can light up my apartment for a tenth of what it costs to run the pigtail floro bulbs.