I agree with Oso. The first thing to do is know the kilowatthours or kWh's that you will need in a 24 hour period.
There are so many other things to take into consideration that are just as important to the overall cost and reliability of the sysytem.
It would be a great plus to your advantage if you have a friend that is a licensed electrical contractor certified in photovoltaic systems or at least an electrician familiar with the National Electrical Code or NEC and how to use the book, in particular Articles 690 and 310.
With all of that aside, lets assume that your kWh's add up to 4. Now you will need to know the equivilent full rated charge hour day that you can expect from a PV array. Go to this web site and just experiment with the different arrangments of PV arrays for your region.http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/atlas
First try; Average, June, flat plate tilted South at latitude - 15 degrees.
Then try; Average, December, flat plate tilted South at latitude + 15 degrees.
This will show you the difference in the number of equivilent full rated charge hours per day from Winter to Summer in you region. You will want to do your PV array sizing using the Winter time hours. I am going to assume 2 hours. Now we can size the array by taking the 4 kWh's or 4,000 watts and divide by 2 and that gives us a 2,000 watt PV array. Now you must choose a nominal vdc. In your case I will assume all 120vac loads via true sinewave inverter from 48vdc. Take the 4,000 watts and divide by 48 and you should get 83 amphours.
Take that 83 amphours and multiply by 5 (which is 20% of a fully charged battery) and that will be a 415 amphour battery at 48 volts at the very least. If you are conservetive this should get you through about 3 maybe 4 - 24 hour periods with little or no sunshine during the Winter months. Consider the cost of a generator.
There is so much more to consider though for a completely autonimous off grid system for $10k.
Know your needs in kWh's then do the math above. Your figures will help you to know what size of a system you will need and if $10k will get that. Dont forget the; charge controller, inverter, electrical; wire, disconects, conduit, fuses, breaker panel, breakers, and so forth (this is where an electrician friends come in handy).
I hope to answer more specific question in your next posting.