We don't know the context for OP's scenario ... brief emergency outage most likely, but what is your context?
Don't forget the value of *reducing* your load, before sizing the solar gear to support said load ... you'd reduce the load in advance, during an emergency, to fit your proposed solar gear budget.
The gas guzzlers currently in use in your grid-connected home (if that's what they are) can easily be bypassed with emergency use equipment for the outage, with way less watts and therefore way less expensive solar gear needed. Have an ice chest cooler on hand that keeps things at 50 degrees or thereabouts; have a small "cooling" device that will help you limp by until the power comes back on.
Alternatively, if forced to stay with the existing fridge during an emergency, have ice blocks pre-frozen and on hand, and operate the fridge at key portions of the day during the outage (but not at night, when hopefully nobody is using it, and letting cold air fall out). Perhaps something similar for the AC.
And, as previously mentioned, you'll have a ($500) learning experience out of it. With careful planning, you might end up with a "parallel" solar gear setup that you can use during an emergency and/or take on a camping trip, getting dual use out of it. Haven't priced such a low system cost recently, but I'd imagine you might squeeze in under the $500 cap, especially if you are willing to learn as much as possible, buy the parts and construct it yourself, and be reasonable with the tradeoffs.
Hope this helps ...