I don't know a huge amount about Arabians, but this is what I've heard, and what I do know. There are Egyptian Arabians, Russian Arabians, Cabberet (sp?) Arabians, and probably more strains that I haven't heard of before. From what I've heard, I believe that the Cabberet Arabians are more sport horse type, versus racing, or saddleseat. Egyptian Arabians have very typey heads, and are finer boned I believe. And are generally more of the race type strain. And Russian Arabians, are a bit thicker, and don't have as typey of a head. Do please correct me if I'm wrong though, as I got this all from a breeder who has kept the mindset of what the arabs were in the 60's. I have a Cabberet bred Arabian, who is bred to be more of a sport horse type Arab.
Polish, Egyptian, Russian and Crabbet are all Arabian types commonly seen. They simply refer to the origin of the horses breeding in modern times.
Polish and Egyptian are most common in the US, Crabbet bred horses I believe come from a breeding program that originated in England. Obviously, all arabians of any type originated in the Middle East.
Egyptian bred horses are supposedly a little hotter and more difficult than the other types, alot of halter horses have egyptian in them it seems. I work with polish bred arabians and in general they are very smart and trainable and don't often have the very extreme refined features that some egyptian bred horses may have, I believe the same goes for russian and crabbet arabians as well.
Of course, many arabians have pedigrees that include more than one type as well.
There are also Spanish arabians, which were developed around the mid-1800's by the Yequada Militar (government branch which directs all horse breeding in Spain). It was a extremely strict program designed to create awesome, athletic cavalry mounts with intelligent, trainable minds. They are excellent sport horses.
Spaniards tend to be more robust, with large bone; deep, wide and round, not a very refined face, but large soft eyes and big powerful butts. My horse is a straight Spanish Arabian and I have to say, I favoured this strain over any other even before I got her and became awfully biased. ;)
I would suggest polish arabs. Of all the types I have dealt with they seem to be the most calm as well as are hardy. Of course a lot of arabs are a mixture of a bunch of different "types" so instead of looking for a particular type, I would suggest looking for the personality and the training that you want and forget looking for just a type.