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.
Wow, thanks for all the info! Because we have a high hawk population I don't think I could have any breeds that need to be let out all the time. I love the look of the fantail, but do worry they'd be high maintenance.
We have a lot of high space in our run, and I'd like a breed that would spend a lot of time up there. Although, I also don't want them to end up pooping on my hens!
American fan tails are great beginner birds and not high maintenance at all. Indian fantails are great to but a little more work if you want to show them because of the feathered feet. Even with that I wouldn't call Indians high maintenance either. Either way fantails would be a great choice.
Ah, the fantails are gorgeous! One issue to consider with any pigeon you want roosting up high is cleaning that area. Otherwise, you get this: http://img1.classistatic.com/cps/po/110326/811r9/8431d07_27.jpeg
So, if your run top is really high up, just make sure you can get to it with a scraper/powered hose/whatever method you choose to clean with so you don't get a bunch of poop and nastiness collecting up there. XD Using perches where the poop just drops straight down would also help, but when perching any cage, make sure perches are not placed directly above any water or feed containers on the ground. Otherwise...they will be pooped in! You might want to put them more to the side where your chickens are not usually out too, to avoid chicken poop targets. The problem with the thinner perches, is fantails are usually kept on layers of platforms since they don't always land as well as other pigeons.
As Timmy said, there are different varieties of fantails, and some aren't bred to an extreme as much as others. "Garden fantails" tend to have the least amount of tail feathers, and are often fantail crosses (ie. homer crossed with fantail). The show fantails, if kept in typical loft conditions where the owners want good tail feather quality, are usually encouraged to be on the ground. The more a fantail has to fly, the more funnel-shaped the tail will become. So, look for more funnel tailed birds with fewer tail feathers (some people do clip the tails though, so you may be looking at an Indian with clipped tails) rather than turkey looking fans if you want a bird that is used to getting around. If you get a fantail that has obviously been kept on the ground, people usually find they need to teach them to perch by holding them on the perches a bit each day til they get the hang of it. Fantails tend to be fairly tame, so they aren't likely to be flapping in your face every time you go in the run. XD Some breeds do spend more time on the ground than up high. Heavier fantails will spend quite some time on the ground, so I'd shoot for a fantail cross myself, and if possible, take a look at the area whatever pigeon you decide on is housed in. Ask for photos if shipping. Ask or look to see if they are always hanging around on the ground, or if they prefer to perch. Pigeons in general spend time on the ground, but with some searching, I think you'll find something that will work for you.
Hope that helps, and good luck on finding the right breed for you.
I have a couple baby Satinettes that'll be for sale once they are weaned off
They'll be at the perfect age for taming. They are already a naturally calm and friendly breed. And the boys have that attitude where they are kittens who think they are lions They're very entertaining