Whippets live quite happily with cats and although they can run fast, they don't usually run away, they are home loving affectionate dogs. Just need a warm coat in the winter and somewhere cosy to sleep as they don't carry a lot of extra flesh. Good choice, go to a reputable breeder and see their other dogs and you will have a lovely pet I am sure.
To whoever asked why crossbreeds are cheaper to insure, its because they don't cost as much to buy as a pedigree (unless you buy one of those designer crossbreeds with a fancy name) so they have to pay out so much to replace them.