I have a very large grey hound in a small house with three other people two dogs and 12 cats I don't find his size much of a problem he loves to share the coach with every one. Mine came from the travelers and with any dog I've rescued from them they are beaten into submission so they learn quickly to stay out from under your feet, pavo as he's called has no problems with aggression (a good side effect coming from the travelers haven't met an aggressive one yet thats not to say there all like the ones I've rescued) He's great with kids and loves hugs from babies even puts his head down for them to reach and is very carefully around my grand mother seems to understand he needs to take special care around her.
They are great fun at happy hour and love to see whats in the shopping bags to nick and love to spend time with you curled up on the couch and most are use to traveling for one reason or an other the down side is of course some have been coursed or train to race after live animals ie rabbits and hares. so may not take to cats' but if you fully intend on being a responsible owner and keep them on lead outside I can't see any problems.
You could look into a female who has only ever been breed not trained and give her the life she's hasn't had yet they are smaller and more inclined to get on with cats most shelters should be able to give you the heads up on it.
Over all I have to say I've enjoyed him and love having him here and the space doesn't really matter as I also have a big back garden they really are very lovable with there big brown eyes making me give them hugs and my dinner. You couldn't make a better choice there right up there with the collies, labs, boxers and many other family pets.
I found this group very supportive in giving me info when I first tuck in the grey hound and they have lots to adopt as well. I'm near sure she said they take in whippets as well.
The lady and gentleman that run this group are lovely and take in all breeds of dog although they are not state of the art yet!!!(I'm helping fund raise to do so) the have the biggest hearts when it comes to animals I've ever met and will put you on the right track with the right animal for you.
Here's a sight that tells you from peoples own accounts of owning grey hounds/ lurchers and info for anyone who's interested.(I had trouble getting into this one but I think it's only my computer.)
Along with paws who are great as well when the time comes keep a close eye on the pounds these dogs need rescuing first before they are pts.
Best of luck in your choice.