Rehoming is great, an older dog is much less work and hassle than a puppy, less of a gamble than a puppy with regards to temperament as it's already an adult and will be assessed by a rescue.
But, it depends on how much you want a certain breed as obviously they only have the dogs they have.
If you have picked a breed and it's not one that comes up for rehoming then you would probably be better looking for a breeder.
Looking for a breeder is a bit of a minefield really.
They should be breeding for a reason other than just selling puppies, so showing or working and have bred to get a puppy for themselves.
They should have done all the health tests for that breed and with a lot of breeds extra ones as well.
They should be registering the puppies with the kennel club as there really is no good reason not to, it's cheap and easy to do.
They should pretty much interrogate you and expect you to visit at least twice, they should be telling you which puppy is best suited to you and not just letting you pick in a first come system and make you sign a contract saying that the puppy is returned to them if you ever need to rehome it.
Good breeders usually have a waiting list and only breed a litter once every year or two, so be prepared to wait once you have found a breeder.
They're also very unlikely to own the father as they should have searched for the best stud to complement the bitch's traits.
The puppies should be wormed, possibly microchipped, they should be able to tell you about the socialisation the puppies have had (there are plans that can be followed...basically a lot more done than just meeting who happens to be around) but, they're not likely to be vaccinated as different vets use different regimes and that can result in having to start the course again.
The best place to start is the breed club for whatever breed you've picked, find out about health tests and see if they have a list of approved breeders. (Some do , some don't)
The only two websites to look at for breeders are the kennel club and champdogs...you'll still have to weed out the bad breeders, but you'll find decent ones as well unlike other websites.