Help a girl with her electricity please?

[Skvez]

Voltage (unit capital V) is a measurement of the desire for current to flow
Current (measured in Amps, unit capital A) is a measurement of current.
Watts (unit capital W) is a measurement of Power or Work done.

Watts = Volts * Amps (assuming a unity power factor, lets not confuse the OP with a discussion of power factor)

Your 1000W inverter might power a fridge (see previous comments about problems starting the compressor), for a little while but it's unlikely you'll be able to keep the battery charged up enough to do so.
You'd need a fairly expensive solar panel array to keep your batteries topped up enough to keep a fridge going.

Before we can properly offer ideas we need to understand what you'd like to be able to do and how much money you have to spend on a solar system.

Things that you can easily do with a fairly small Battery back-up system
Lights
Radio

Things that require a moderately big (Expensive) system
Computer
Fridge

Things that are not realistic for most of us to consider with a Battery back-up system because it would be just too expensive (and there are cheaper ways of doing it)
Heating
Cooking
Hot Shower