Whippets are playful but gentle dogs. Rough handling, even in play, is an absolute no-no and you'll get the best training results with treats and praise. They respond very poorly to force-training.
Sighthounds are traditionally considered rather aloof dogs, but Whippets are an exception. This is one of the most affectionate of breeds; most of them love all the petting and belly rubs you'll give, and many are real snugglers. We do meet the occasional reserved Whippet, but in our experience, over-exuberance is much more common. The "Cool Joe" Whippets are very loving, too, just not quite as physical.
Whippets are sometimes referred to as "Velcro dogs." You might have more company than you want in the bathroom, and if you go out to the mailbox, you may be greeted just as enthusiastically upon your return as you would be after a two-week absence. This is more togetherness than some people like, and if you really prefer an independent dog, a Basenji might be a better choice.
You'll be wise to keep your Whippet close to you, especially at first. Whippets are mischievous! Clever and cute (but annoying) behavior such as leaping to the kitchen counter and scouting for food or tearing up a sofa cushion to make it softer is common, especially in puppies and young adults. Whippets do mellow out around two or three years old, but as puppies, they can really be monsters. This is not a pup you want to leave loose in the living room while you run to the store!
Whippets will want to share your bed as well as the couch. In fact, if you are really fussy about dogs on your furniture, you might want to reconsider choosing a Whippet. A Whippet in good condition has very little "natural" padding and hard surfaces are distinctly uncomfortable. You'll seldom see one willingly lying on a bare floor. Whippets love their comfort; the softest chair or pillow your boy can find probably will become his favorite. If you use a crate, provide a soft mat. Like cats, many of them seem to enjoy perching in higher places...the back of the couch, the top of the sideboard, even the dining room table. Obviously, some training is required!
Crate training is a good idea for your puppy...you have to take a shower sometime and the little scamp can get into all manner of things while you're occupied. However, the desire to be around people also makes some Whippets hard to crate successfully; some howl and moan in their crates even if properly crate-trained as puppies.
Separation anxiety is discussed as a breed problem, but as in many others, it is often over-diagnosed. Whippets who are unhappy with their living arrangements tend to let you know about it. I've heard many a story about a Whippet with "severe separation anxiety" who is fine when placed in a home where he receives more attention.
~Thanks to Timbreblue Whippets
for the use of this material from their website.