You want a shorter horse (around 14.3-15.3 hands) with a short back, longer legs and good balance.
Hahaha---colour makes absolutely NO difference in the quality of the horse what so ever.
Quarter horses are the most popular--if you are looking to get into pro rodeo and barrel racing, I would say (if you can handle it), get an Appendix Quarter Horse--they will have the muscling of the QH and the speed of a TB---hybrid barrel horse if you invest in the right bloodline---a horse that is going to take you to the pros isn't going to be cheap at all...you're looking at, at least $30,000 or above (and $30,000 is a bit on the low end of the price scale..)
I actually prefer geldings (although my past 2 barrel horses have been mares...but good mares at that)----with mares you gamble with them being "moody" when they're in heat....which seriously cramps your competition style, I've been lucky to not have "moody" mares, but I know a lot of people who have moody mares and they consistantly have to withdrawl from competition because the horse just will not cooperate during that time of their cycle...
For this reason, geldings are much nicer, and generally a LOT more reliable....I would strongly advise against a stallion, as they are incredibly hard to train, work around, stable, and control....a gelding is definitely your best bet, unless you are purchasing a seasoned barrel mare and you are certain she will not become moody on you...
Have you rodeoed before? How long have you been barrel racing?