I would see if you can be tested to find out exactly what it is about cats you are allergic to - most people react to a protein in the saliva, rather than the hair/dander itself - of course because a cat grooms itself frequently, that protein then gets all over the fur!
If it turns out to be the saliva, then a long-haired/shorthaired/curly haired/hairless cat isn't going to make an awful lot of difference - but you could look into Siberians - I believe they don't produce as much of that particular protein in their saliva as other breeds.
Incidentally, when I got Radar my first ever cat I thought it was going to be a nightmare, I didn't know I had an allergy, but as soon as he got near me my eyes went all red and itchy and I started sneezing and coughing. It gradually got better as my body got used to his presence. Then it happened all over again when we got Sonic! I don't get any reaction from either of them now, except if I get even a slight scratch that doesn't break the skin then it really turns into a red welt.
Keeping them out of your bedroom is a good idea for those with allergies (if you don't ever let them sleep on your bed then they won't miss it, just make nice appealing sleeping places for them in other rooms - radiator beds are great), and wiping them down regularly with a damp cloth can help too.