Have a look in the gallery and you'll see piccies of my blue bi-colour ragdoll kitten.
Persians are cats you have to groom at least once a day, and are relatively self-dependent.
Birmans only come in colourpoint or mitted. Colourpoint cats have coloured faces and paws, and don't actually have any white, the rest of their bodies are a very light variation on the point colour. Mitted cats have white chins, front white mittens and back boots. They like attention and like to follow their owners around a lot. They can spend quite a few hours alone, although if you are going to be out all day every day you should get more than one as they get lonely. A birman has a rounder head and eyes than ragdolls.
Ragdolls are the ones I know most about

They come in 3 coat patterns, colourpoint, mitted and bi-colour. The colourpoint and mitted patterns are the same as Birmans, but the bi-colours have a white inverted V on their face and quite a lot of their bodies are white.
Ragdolls CONSTANTLY need to be around their owners and love attention. They flop over in your arms, which is an amazing thing when you're cuddling them, although can be scary if they are sleeping and breathing lightly!!!
They are sooo laid back - my kitten is currently cleaning himself in my lap while cuddling at the same time

He has also been great if I have a bunch of friends round - just wants attention from everyone.
They need attention though, you either need to be around a LOT or need to get a second one.
Ragdolls are quite active as kittens and still relatively active as adults. A lot of them are big purring lap cats (my Jack included). You do need to groom them quite frequently, as they shed quite a bit in spring/summer and they can get matts if you don't groom them at all.
Ragdolls grow larger than Birmans, and I think have slightly longer coats.
Which you get really depends on your circumstances. If you have a lot of time and attention to give then by all means get a Ragdoll or a Birman. Have a look at bi-colour cats and see what you think of those, although I think mitted cats are just soooo beautiful!
You can also get lynx point cats (not so sure about Birmans, but definately Ragdolls), which have the colour broken up on the face in a tabby pattern.
I love my Ragdoll and wouldn't trade him for anything, but obviously the breed isn't for everyone. I considered Birmans and Ragdolls, but the Ragdoll breeder was the one with kittens at the right time
EDIT: seal and blue are just colour names. Other Ragdoll colours are lilac (dilute blue), chocolate (dilute seal), red and cream (dilute red), although these colours are more common in some places than others.