I'll take a stab at this as I have several websites in the works that will hopefully be a reference for questions like this...(ps...stay tuned!)
Some of the bloodlines within the Arabian breed are:
Babson (and Babson/Turfa, Babson/Turfa/Sirecho, Babson/Brown)
Blue Star and Blue List eligible
Early-American and American Foundation
These are in no particular order and if I forget anything I did not intend to offend :) Defining their types would be hard as each group can have a wide variety of types within it.
Fire N Ice is sired by Gold N Ali that was predominately Crabbet/CMK, his dam was heavily *Bask bred with a touch of Crabbet/CMK.
Black is not that uncommon and there are many breeders that specialize in it. Hughes Arabians and Flying A Ranch Arabians are both known for having quality black Arabians.
Hope this helped a bit!
As for temperament, are they different with each bloodline?
What about show jumping? I am thinking of getting into it whenever I get my first horse(Which isn't anytime soon.=(
Which bloodlines are best for it?
What are Arabians like in show jumping?
I read a book about different famous Arabian stallions and one was(well looked to be) all white, but was a very light light grey, unless it was just the photo. The photo was an old one, it was in black and white. Well anyways, I can't remember his exact name, but I think it had the word Prince(I think) in it. I will check the book out at my library and see if I can find it.But apparently he was a famous Arabian stallion. I think it said he was an Egyptian? He is nice looking. I don't know if anyone has a clue who I may be talking about.lol
Everyone please keep the information coming!