Welcome, and yay on a new betta!
In my opinion, the question would be "Am I prepared with everything I need?" :)
There are no major differences between any of the tails other then the looks- and when it comes to that, it's each person's preference. But there are slight differences to each:
CTs are slimmer in body and tend to bloat easier then the others if not fed appropriately. Halfmoons can be notorious for biting off their own fins, mainly due to the heavy drag (but tail biting is not exclusive- I have a veil that tail bites).
Veils are usually over bred and not bred for genes since they aren't as popular as the other fish. (Given time that will change, as now a lot of other tail types are becoming more available instead of the usual VT)
But other then those considerations, it really is up to you and which guy speaks to you when you look for one. I thought I wanted, needed a CT a few months back- so I went and got one. Ends up even though I really wanted one and found a great one- my fave continues to be my older Veiltail. Grumpy old Xander is just the basic blue on black, but I just love him and until he made a new girlfriend, Anya (>.<) I was his whole world and we created some form of a bond.
So in the end, it doesn't really matter the tail type, but who you fall for. Doesn't mean you won't have a preference, just wouldn't "plan" on a certain one until you see them all at the store :)