Depends what qualities you like (tameness, curiosity, looks, etc.), and if you want to use them for any purpose other than a pet (ie. flying a kit of rollers, etc). If you can, definitely, definitely attend a National pigeon show. Huge selection of birds, breeds, and breeders to talk to. Seeing the different breeds in person helps you get a feel for them and what appeals to you much more than photos and so forth. But, I can tell you what breeds I've been most interested in for house pets (so, qualities I'm interested in are tameness or how much personality they seem to have).
-Mookees (A lot of people seem to get them for their kids. I hear they are a good beginner pigeon, and tame down well. Many like the head bobbing/zitter quirk, though not all will display this)
-Rigneck dove (My husband has one. Gentle, and pretty tame. His bird is kind of sassy and is fun to let run around the house. Easy to find too. Most pet stores have them. They have a call that sounds like a laugh...really cool. Make good foster parents as well for pigeon breed that have trouble hatching out their own young)
-Lahore (Large birds, but very tame. Have soft, almost mammalian looking eyes. Beautiful birds.)
-Parlor Rollers (My first choice for a house pet. Can't fly as adults, and I've seen some amazingly tame pet parlors. Their history and behaviors are fascinating, their look variable.)
-Modenas (Will be looking into these later in life as an outside pet. The chicken pigeon. XD We got a chance to compare poop at the pigeon show, since that is a concern for birds we will be keeping nearby. Lahores are big birds, but their poop was dry. Modenas, a bit bigger, smellier, and messier. Kings had awful, wet, huge, smelly poops. They were from multiple breeders, so I am assuming it is a trait of the breed, or their lifestyle.)
-Shakhsharli (didn't get to see these at the show, but they are beautiful, and I hear they are very tame)
-Taganrog Tumbler (My husbands first pick. He wanted them even before the show...but now he wants them even more. XD He also liked the various homers, especially the...I will have to ask him if they were the Exhibition, Show, or Giant. Whatever they were, some were a bit nervous, but most seemed pretty tame.)
I've heard other people mainly prefer the croppers and pouters for pets. A lot of people like the various rollers and tumblers, but I personally am not too interested in most, like Birminghams, until I can fly them. Fantails are also popular, and trumpeters. I wouldn't want to mess with cleaning and managing the feathered feat of the trumpeters though! At the show, they were tracking through their own poop with them, and a few had broken some blood feathers. I could just see them tracking through my paintings and having that end badly. XD Oh, and the German owls I've seen as pets before. The Orientals were *really* flighty, but a lady had a hand raised one that was sleeping and crawling all over her. Which brings up my next point, if you want a really, really tame pigeon, regardless of the breed, the tamest and most human-affectionate birds I've found have all been hand reared. But, it sounds like maybe you are more interested in having pretty birds to look at that having really affectionate pets? Just make sure the breed you love the look of can tolerate your climate well, and decide if you need a breed that is able to avoid predators better or not. I personally thought the Starlings were gorgeous...but they were all very flighty at the show. Those only came from one breeder though.