Just a little above your stated budget--but well worth the extra umphh ...
I really am high on this one. (Own it and use it myself.) Have a look at this beauty ... the AEB OX Mini Power Plant Solar Generator
A lot of power in this package ... beyond anything else in this ballpark. We've sold a LOT of these and everybody is thrilled with it. BTW, the buyers club member price on this is $2399, shipped. You can charge this unit from 110 or 12V. The clincher, but at additional cost, is the hinged Kyocera solar panels that go with this--at another $1279, member price, shipped.
And if you want still more power--the Piggyback units are available too. It's all plug n play right off the pallet.
Cheaper, smaller solar generator units are available out there close to your price range. You can look at the Humless Sentinel + Solar Panel Kit
. This is a complete solar generator kit at member price of $2300 shipped. However--beware that you probably are not going to get the utility out of it that you want when you mention household appliances, water pump, etc. (check the power draw on those necessary units).
Smaller than that, when comparing to what can be had for just a bit more money getting into these two units I've mentioned, I have a hard time working up my enthusiasm. And I am doubtful that you can find any real power for your appliances in a complete solar generator package. If you're going to get a solar backup system, you probably want to to provide some practical and useful power, otherwise--what's the point, right?