Hi MrMud,
For 3500 you should be able to get 1000 watts of solar (parts only). That, in mid summer would provide for 5000 watt/hours of power per day. In amp-hours that is 833 amp-hours.
It would likely produce all the hot water you could use assuming a 10 gallon electric/propane water heater, and run the fridge too. After the battery bank was recharged it would be possible to run a small air-conditioner, on an almost 1:1 basis (solar power running the air-conditioner)
In the dead of winter you would get about 1/6th of that amount or 138 amp-hours per day, assuming a not tilting installation. That would be enough to run the fridge assuming there is enough storage capacity in the battery bank.
The problem may be one of "real estate" on the roof. It might be an idea to have one set of amphorus panels (the Uni-Solar type) and one set of high efficiency mono crystalline panels. The amphorus panels will react to much lower light levels--and extend the charging day. However they are twice the size of the other type.