There are a lot of breeds but some of the underlying things don't change -- "cobby" bodies that are more thick-boned, like british shorthair and persian, will be more relaxed and lovey, very "sweet" in how they react to you. The more angular the body becomes, the more active the cats get. Orientals and "wedgie" Siamese are marathon athletes, while Persians are fluffy couch accessories, in other words
My wife and I did "the hunt" this summer when we were looking at what kind of cat we would like. We had a few ideas but most of it comes down to what you can find in your area, unless you're really in love with a breed. For instance, we loved the look and size of the Singapura breed, but good luck finding one!
Anyway, Juniper is an Abyssinian and Bixby is a traditional Balinese (a Siamese with long hair). Juniper is pet quality because he has some tabby marks, which also made him cheaper, but he's still registered because we love him. More to the point, even though Juniper isn't "big," nor will he get really big, he's just a ton of fun. He's a total clown most of the time, but also extremely muscular and athletic and his preferred method of play is jumping. He'd rather leap and twist and flop at something than actually catch it -- he loses interest once he's actually caught a toy.
But because he came from a good breeder, he's also well adjusted to people. When my wife and I watch a movie, after about 15 minutes he comes and sits on us, usually my lap. He seeks us out and wants to be around us. That also means that we can't sleep with him in the bedroom or else we'd never sleep, as he'd want to play at least every hour.
Bixby is much more calm, and not just because he's 2 months younger. He's a much more gentle cat and doesn't struggle to be picked up or moved -- Juniper usually decides that being moved means he wants to run around. He'll probably end up larger than Juniper but still pretty lean.
Bixby's too new to have any real dominant traits stand out, other than he's a squeaker who talks for the hell of it, but quietly, and he's turned into a "little brother" to Juniper, as in he likes to start trouble but then tries to make it look like he's getting picked on! He's much more sweet around people, though, as he's able to sleep in our bedroom without chewing on our toes all night and typically we wake up with him nestled between our pillows.
One thing we like about both cats is they lack an undercoat. Juniper's fur is thick but very, very short. Bixby's hair is long, but not very fluffy. He's more of a sleek poof. As such, both basically don't shed (although they're also spoiled for quality food, which def. helps).
Most of what makes a good cat, in my opinion, comes from having a happy kittenhood. That's one of the reasons my wife and I value pedigreed cats so much -- we can meet the breeder, who has handled the cats and helped raise them, and we can meet the mom and the littermates. We know the cat's been around other cats and knows how to play, and that they've been fed good food and gotten lots of playtime and motherly instruction. There are awesome cats at shelters as well, but it's a little more random and depends on the quality of your local shelter/spca.
The best thing to do, if you're looking for a pedigreed cat, is to simply go to a cat show. You'll see all the cats you're currently only seeing in pictures, you'll have a chance to talk to breeders, and also see what's generally found in your local area. My two pedigreed cats (one CFA, one TCA) are incredibly fun and with a great personality that's exactly what we had hoped for -- energetic but lovey. We love the high energy because we're not generally people to just sit around, but are moving around the house and doing things. So we wanted our cats to be active as well. Although truthfully most cats will end up pretty lovey to their owners.