The Assured Breeder scheme is not fit for purpose. There doesn't seem to be any serious policing, so any person who wishes to breed dogs for profit can apply to join the register and be pretty confident that no one will ever come round and inspect them, their premises or their dogs randomly.
Whippets are lovely dogs, not too heavy to lift when in later years they may need help in and out of the car.
Incidentally, these days a lot of owners of larger, older and less mobile dogs use a ramp so that their dog can walk up and down into the boot, so don't let that aspect put you off any particular breed.
Amongst the many many dogs I walk regularly there are a pair of greyhounds. One is not less than 12 and still happily bounds into the back of the car without help. The other is a youngish ex racer, although his owner lets him off lead when she's sure it's safe, she has requested that we don't let him go, as he was trained to run flat out after furry things and there are lots of hares and deer around here. And I've experienced him sighting and accelerating towards a cat, it was a pretty powerful lunge and nearly had me over!
Be particularly careful if you're considering any of the currently fashionable breeds. Mini dachshunds, pugs, cavaliers immediately spring to mind. Unscrupulous breeders will always try to fulfil the demand for whatever breed is currently selling for £1500+ by over-breeding their bitches and using any stud or bitch that looks okay without getting health checks.
Some of the more established cross-breeds breeders are possibly better at self regulating themselves than breeders of official KC listed
breeds. I have a friend who has been involved in cockerpoos for 25 + years, she and some others keep a scrupulous stud book to avoid in-breeding, and for several generations now the litters have been both parents cockerpoos and are coming out true - there are no longer throwbacks of dogs that look far more spaniel or far more poodle than anything else, and the desired coat seems to be settled. However she is just as aware as the rest of us that anyone can say something is a cockerpoo. One that we walk has a lovely temperament but is a physical mess - awful confirmation and arthritis already evident at just 2 years old. And far far too big. Owner has said she now realises she bought him from a puppy farm and wishes she'd realised just how far these people will go to make it look like it's a respectable home-bred litter. We think although one parent probably was a poodle the other was something much much bigger than a cocker spaniel.
The actual breed societies are probably the best people to work through - and the specific breed rescues even more so. There are groups which work to rescue and rehome various breeds, I know of one for border collies, obviously the greyhounds, there's a bunch called Spaniel Assist, and I work directly with Black Retriever x rescue which is involved with lots of purebred gun dogs as well as their accidental litters. Having helped pick up the pieces, they will know a lot about who the bad breeders are so you can avoid them.