I have a 2 year old whippy and know many more, I think they are great dogs.
Some points.
They are very good with well behaved chidren but do not tolerate pain well, so while a lab or Stafford may well look on benevolently as a child climbs or steps on it (not that I think any child should be allowed to do this) a whippet is far more likely to growl and be unhappy. Sadly my ds was very badly bitten by someone elses whippet at the end of last year for no apparent reason, up to then the dog had been very accepting of children, but this can happen with any dog.
Working lines will be far more prey driven than show lines and I wouldn't go that route if you are looking for peaceful walks!
Generally whippets are extremely loving and very attached to their owners, most will tolerate being left but they don't like it, some develop bad seperation anxiety and can be extraordinarily destructive, they can take a lot of patience to get over this. Generally while walking though it is an advantage is they really just stay glued to your side or if you wind they up (very easy 
) they will take off in wide circles, but they don't run off iyswim, just big happy rings around you.
They will chase, but I can call mine off of anything, including squirels, but you will be looking into doing a lot of work to do this and it will ultimately depend on the dog. I would recommend 'Pigs Might Fly' if you haven't read it already for training stuborn dogs. They are not natural retrievers, but if you think outside the box they can be trained to retrieve, mine is now ball crazy, which is great as it is wonderfu exercise and chasing for him, you will need a flinger, otherwise the ball tends to not go far enough and they can injure themselves.
They can also do obedience, agility and fly ball, but sight hounds are a law unto themselves and require different training to a Lab or Collie, you need to train somewhere where that wi be taken into account. They are extremely sensitive and training needs to be gentle, fun and positive.
Running injuries are not uncommon and broken legs do happen, do get good comprehensive insuance. Rips and tears to the skin if you walk them anywhere with anything pointy (hedges, walls, bushes.....) are quite a common occurence and while the first couple will send you running to the vet, you will soon learn to dress them yourself .
Mine is fine with cats, but again only through exhaustive training, as we don't have a cat ourselves.
They can take a fair time to grow up, expect puppy naughtiness up to around the age of two and they are terrible food thieves, tall enough when standing on their back legs to reach the back of a kitchen work surface. Mine looks like an angel when people are eating he would never beg or take food, just curls into a tiny ball on his rug, but the minute food is unattended all bets are off.
They can be picky with their own food, a raw diet works very well for them or a very good quality complete, some are very hard to keep weight on, occasionally some go they other way are run to fat but this is rare. They are very sensitive to anestethic due to their low body fat and you need a vet with some experience of sight hounds, nearly all whippy puppies are diagnosed with 'heart murmers' by inexperinced vets, they always grow out of it. They are generally very healthy and rather long lived.
They feel the cold and will need probably need coats in the winter if you walk with them or are doing anything that involves standing around, if they are running they are fine. They need to wear a sight hound collar and preferably a wide fabric martingale as their heads are smaller than their necks and they can back out of normal collars. They need a comfortable bed and lots of blankets but would really prefer to share yours, if you are not happy to let them share the sofa they are really not the dog for you. They do not like the rain and mine even now will go and poo in our bathroom next to the loo if it is raining 
he would never pee in the house though. They are mildly eccentric and can be kleptomanics, you will find all sorts of wierd and wonderful things in their beds that they have 'collected'.
Sorry, that's a bit of a massive essay 
. When you want some more information either Citycroft or Stormburst are both brilliant breeders with loads of experience and will be happy to chat whippies with you and tell you anything you need to know.