Thank you!!! I have read this twice. I am SURE that three is a charm.! SO often I realize how really niave (and lucky) I am in using equipement that I have no clue about.
I guess I overdid it. :)
The bottom line is that, while there is no general answer to your question, there is a specific one. If know what equipment you want to run, how low a voltage it can stand, how much current it draws (all on the data plate somewhere, or in the user manual) you, or your electrician, can easily determine how big (what diameter/gage) wire you need.
After all the power line feeding your whole house can be though of a big extension cord. If it's an overhead, rather than the now more usual underground, one, then you can go look at how big *those* wires are. I think you'll find they are pretty big.