Check out the International Betta Congress website for the latest info on accepted colors and finnage. Yeah good show bettas can be major $$$$ lol, there are definitely breeders out there! I thought about getting into showing and breeding but I decided to stick with rescue and keeping them as a hobby (years ago I actually belonged to a now defunct, huge online rescue/hobby community - I bet there are more out there for those interested).
Now please realize, my interpretation of accepted colors and faults are just from a hobbyist point of view and I’ll be honest it’s been years since I’ve looked at IBC so my knowledge is probably out of date, but here’s some showing info I know: common color faults are red wash and blue wash. Blue wash on reds and chocolates are common faults, and red wash on white and turquoise bettas is a common fault (but ALL white bettas will redden to some degree with age…my gorgeous DT male was a white betta with black lace on his body, with the tiniest dot of red on his ventral as a young’n, but by the time he died at 5 yrs old he was almost completely red).
Veil tails are genetically the “mutts” of the betta world and are not able to be shown and for breeding purposes are sadly worthless (fine pets, though, I have and have had many!). Veil tail is not an accepted tail type and I can’t imagine that’s changed. Crowntails and combtails used to not be able to be shown - not sure if that is still the case because they have become wildly popular.
Crowntails are considered the most aggressive type of betta.
Bicolor bettas must have clean separation of colors. For example a good butterfly pattern on a betta must be clean with unbroken lines and even spacing. A good red Cambodian must have reddish fins, but no red on the body.
Finnage must be full and perfect, evenly spaced with no tears or holes. A halfmoon must be a perfect full half circle, for instance.
There are also lots of different types of bettas than just Betta splendens, so you might be interested in checking out the different betta species. Betta macrostoma are really cool-looking.
Welcome to the hobby! 