A good bank of batteries (preferably deep cycle, like marine or golf cart batteries) is best, these can be charged through a bank charging system, connected to the mains, Or Solar panel, or wind turbine, or harvested from a stream or river using hydro turbines, or a generator (redundant there, since you could just power from the generator directly)
Ideally you would also have a break-over switching panel that connects the inverter to your house circuits.
Such a panel would have to be wired in by someone who knows what they are doing. what it does is ISOLATE your house from the power companys lines into your home. and transfers to receiving power from your "In house" power supply.
That is if you wish to run a few selected outlets in your home from the in house bank.
Otherwise, just run (heavy duty) extension cords for essentials (big screen tv, xbox, margarita blender...)
Many use golf cart batteries in pairs, (they are six volts each)
that way if a cell fails in a battery they are not replacing a full six cell 12 volt battery, only a three cell six volt unit.
It can be quite a spendy thing,
it can be done on the cheap.
After hurricanes Ivan (and consequentially Katrina)
Damaged our home in Florida we all pooled our resources, food, gas grills, coleman lanterns, radio gear, chainsaws, etc.
a couple of folks had inverters that clipped onto the cars battery, we all learned that they can suck a cars battery flat in no time at all.
generators were shared, those inverters ran a small fan (so we could sleep at night) clipped to a battery set on the floor, then during the day, those of us lucky few with generators (and fuel to power them) used the 12 volt ports to charge neighbors batteries.
Back to topic...
You can just run car batteries and connect the inverter, but they use a lot of juice.
Also keep in mind that some electronics, (laptops, cellphone chargers, gaming systems) will run on such an inverter, but they will overheat, and in some cases fry your electronics.
the reason is that the 110 Volts being produced is a "clipped" or "square wave" 60hz as opposed to a "full wave" 60hz.
that that means to the electronics is that there is a brief interval (60 times a second) where the electrical power is not flowing smoothly (on an oscilloscope this can be seen as more of a square, sharp wave. electricity from your outlet is a true sine wave, undulating sensuously across the screen, full bodied and oh so curvy.
This soothes your electronics, keeping them happy (who wouldn't be?).
The square wave that is artificially generated actually induces heat into the electronics.
The Harbor Fright unit reads as a "Modified Sine Wave" that might not be any easier on the electronics aspect of things. But please read the fine print on that and see if its really compatible with electronics.
If you are only going to run appliances that do not have electronics, refrigerators, manual control (not electronic keypad) air conditioners, household lighting, and the like you should be fine.
Hope this helps somewhat.