Have a go of the KC Find a Breed quiz, it's not perfect but it's a reasonable starting point to narrow down the list of potential breeds a bit.
Personally I don't think you can beat whippets as fabulous family pets, they're absolutely wonderful little dogs possibly biased, I'm currently sharing my sofa with three
From the KC breed info page:
"There can be few breeds with more delightful charm than the dainty Whippet.
Carrying a short, fine coat, cleanliness is the Whippet’s hallmark and it is easy to get him tidy enough for the house within a very short time after returning from a country walk in winter.
The description of his temperament in the official standard – ‘gentle’ and ‘affectionate’ – is a considerable understatement; he loves the company of mankind and is equally at home in castle or cottage. Light enough to pick up when necessary, but spirited enough to spend a day on exercise, with a tremendous turn of speed over short distances, he represents one of the most deservingly popular of all the sporting dogs."
All that is absolutely spot on. I'd also add they can be (very endearingly) mischievous, they're very much fair weather dogs (mine go on strike if it's raining), great with kids (my 8 year old niece can happily walk and play with mine) and they are the cuddliest things ever. It's impossible to sit down in this house without ending up with a whippet on/up against you 
They're very flexible when it comes to exercise, mine haven't been out yet and they're all snoozing very happily. Given the opportunity though they will happily go all day.
You do need to work hard on recall when they're little and constantly reinforce it when they're adults but all the whippets I know (and I know a lot through showing) can happily go off lead.