Well it is best if you live somewhere with net meetering. Net meetering is basically a state by state law (and in some other non US countries) that requires that the utility company compensate you for any excess electricity that you pump back into the grid.
So this is why the majority of solar systems are grid connected systems, simply because it is cheaper to store your excess electricity with the utility company than in a battery bank. Then at night and on cloudy days, you simply draw from the grid, and because you generated more electricity than you used during the day, your net usage balances out (if everything is sized correctly).
Now if you want to be totally off the grid, then you will have to get a battery bank and store the excess electricity for later use (nights, storms).
If you want to be totally off the grid I woudl recommend a combination system with wind turbines and solar panels (and maybe even hydrogen- *see blog* )
Now the solar panels shouldnt make the house hotter, I mean you probably have a dark colored roof right now that absorbs all of he suns rays, and this is why the attic spaces are usually so hot (in summer). Generally they are mounted off of the roof about 6 to 12 inches anyway.
In fact now that I tink about it, becasue the panels will be hot and they will shade the roof, a breeze will probably flow beneith the panels causing the roof to be a little cooler, hence making the attic space a little cooler (in theory).
They dont have to be mounted on the roof, they can be mounted anywhere, or you can even get the ones that look and act like shingles.
As far as your last question, the key is to first make your home more efficient, then conserve energy where you can, and then and only then look into an alternative energy source.
Check out the home site, I have written tons of tutorials on how to do all of this: http://www.neutralexistence.com