You will also want to consult the 4-H handbook (available online if you don't already have one - I will gladly post the link if you need it) as to what is acceptable/allowed and/or required for what you will be doing.
If the horse works well in a snaffle then ride it in a snaffle. My two both ride in them, French links. One is 10 one is 4, jumping, trailing, dressage and flat- all in their snaffles. Posted via Mobile Device
OP, you are going to have two different bridles, right? One western and one English? If so, keep the snaffle for the English bridle and I'm not sure about the western. I'm not even going to mention a kind of bit as I have no knowledge at all about western riding that would be helpful.
If your horse works well in the snaffle, use it for everything. You will want to check with 4H regulations, though, as they may require a curb for barrel racing. In that case, I might look into a dogbone junior cowhorse.