Ho Anna,
Your photo is a Cepaea nemoralis - mine is a rare variety that doesn't seem to have any specific locality to which it is found so I suppose I was lucky to see it crawling on our front lawn!
The species that's usually eaten is Helix pomatia, I wouldn't recommend eating any other but that (in fact, I wouldn't eat a snail anyway and certianly not from the garden, bearing in mind how much people use slug pellets which bioaccumulate).
Snails were the first animals to be farmed, by the way - about 10,000 years ago. The Romans introduced Helix pomatia to Britain when they invaded and it still survives in a few places but I believe it's now protected.
Goodness, and it's martle's escargot platter and pricking fork that started this! I shall gird my loins, attach a night light to my forehead and venture forth, armed with cabbage leaves to trap the little varmints, then feed them bran. Well, as one vegetarian to another vegetarian gastropod it seems the very thing to do.
Did Noel Coward have a song about them?
Now don't let's be beastly to the snails,
Don't be horrid to the Helix Pomatia
He knows his shell is horrid
But his sex life is quite torrid
With the lovely, lovely, Helix Croatia