Have to agree with the terrier comments. I've had a West Highland and now have a Scottish Terrier (with a four month old baby) and it does have to be said that they are small dogs with big personalities. He's fine with the baby (even now she's started pulling bits of him) but they are dogs that need to know you're boss, otherwise they get too cocky. I love him to bits, but they could dominate an owner less familiar with dogs.
I'm not sure what everyone means about dogs from private homes? Do you mean people whose bitch has just bred, rather than people who are doing it professionally?? Just because you buy from a professional, doesn't mean they're a kennel. Both my dogs have come from professional breeders (who were farmers) in South Wales. A professional is more likely to have ensured that both parents are disease free and not suffering from one of the inheritable ailments common to the breed. My uncle, for instance, bought a Lab from some bloke he worked with, who just happened to have a litter - and it has terrible problems with hip dysplacia.
Bear in mind that if you get the puppy at two months, it will be another month before you can take it for a walk (after its second round of jabs) and in this time it will be regularly producing stinking piles in your house (or garden, if you're lucky enough to get him out the door fast enough). Different dogs housetrain at different speeds, but you could expect to still be finding wet patchs when he / she is five months old.
You'll have to work on bite inhibition (puppies don't realise that they hurt humans initially because dog skin is tougher and they're used to playing with their litter mates). While you're doing this, you can expect to get hurt - and their teeth are like razors. My dog opened up a cut across my palm when he was little. You can't punish a dog for something like this, because it just doesn't know any better.
While they're teething, they'll chew your chair and table legs. It will probably try your shoes as well, because it wants the comfort of something that smells of you (a habit we've discouraged on all counts).
And then there's the amount of exercise required by different breeds to consider - and how much time you have to give to it each day (walking in all weathers, coming back with a filthy dripping dog, minging of sheep dung... or maybe that's just mine.)