First I think you have to say what level of show you are going to? Are you just going to your county show again or are you going to try for your state fair there? If only going to county show does your county break them down by breeds, or do the steers just all show together. Reardless I think I would cross the Galloways off my list, nothing against the breed, but I dont know any show giving Galloway steers their own class so they would most likely show with the AOBs and I think you would have a hard time finding a Galloway to beat some of the other steers that would be in there at the State Fair level.
If you are in fact showing at the State Fair level, then any breed could work. Remember that at the State Fairs the Cross, AOB, Simmi, Char, Shorthorn, Maine, Chi steers are ussually the tougher divisions. SO you may want to consider one of the other breeds that gets its own breed. It all depends if you are trying to make yourself more competitive or if you are just looking for a breed that you enjoy.
I have no idea how competitive or big your county fair show is. If like a lot of counties it doesnt break the steers into breeds, then I would say one of the breeds I named above as the tougher divisions at state fairs are going to be your better divisions.
All that being said, it is possible to find good ones in all breeds. I think the first thing to consider is your budget, the lesser contested breeds are often a little cheaper to be competitive in. The most important thing I think is for you to pic a quality calf and do the best job you can with it. Learn along the way and in the end be happy with your efforts knowing you did the best job that you could.