Amy
We lived off grid with the bare minimum 6 solar panels 20 batteries and a trace inverter. We lived this way for 5 years. We live in high mountains of Arizona so we have a lot of sun shine.
My sons family (7 of them) and us lived there. My husband said 5,000 will charge the batteries. We had a 7,000 and he said it did the minimal for us. He said it took 3-4 hours to charge the batteries on cloudy days.
Also he said it will not run full sized fridge, a stand up freezer, a washing maching. These will take down your batteries in no time at all. We also kept oil lamps for times we might need them, like several days of clouds or storms.
My daughter-in-law had a Staber washing machine. They have parts that are easy to fix.
Whatever you do-DO NOT plug washing machines etc directly into the generator. We found out the hard way from a local repairman that this will eventually ruin your appliances (and it did), they need to go through an inverter.
I had a 50's gas cook stove that had been refurbished. I loved it out there, as sometimes we had to heat our water, and was great for preserving garden vegetables by canning them. This did have a pilot but no glow bar that requires electric to start your stove.
We both had RV propane refrigerators (because we could find used ones fairly inexpensive). We tried a freezer but our system just would not keep it going long enough. We mainly canned food. We were 45 min. one direction to a one grocery store town and 60 minutes the other direction to a wal-mart, etc.
Another thing to consider is the noise. When we had to run the generator we would get tired of the noise and it was not near our homes it was at the battery shed.
When the generator was running I would use my kitchen aid mixer, run a vacume, sewing machine, grind wheat, watch a movie, etc.
You must also consider how your water is getting into your living quarters. We had a very large tank that required the electric pump to fill it. Then it was gravity to my DIL but I was up hill so had an RV pump to get it into our home.
We learned to work around all these things and basicly you just timed when you did things. The thing that really got expensive was the cost of diesel fuel and we could barely afford to run a generator. We wished we had got a propane one as they were more efficient.
Hope this helps