If you are picking a fish as a pet then it really is up to you, there are certain things you may want to look for if you want something specific, for example, if you want a red fish, what sort of red?blood red?fire engine red?or maybe green, the ideal is a deep forest green. In terms of finnage I know with some pet stores it's hard to see the fins in those tiny cups, but try your best!for crowntails look for nice even rays (the bits that stick out), plakat's I'm no expert with, but I would say look for one with a nice even spread, Halfmoon's, you dont want one with with too long an anal fin, look for one with an anal fin that isnt much longer than the bottom edge of the caudal, or one that ends exactly the same height.(HMPK is basically just pk and hm put together so employ both ideals for this) Delta tails again, I'm no expert on so the only thing I can say here is even fins (same with super delta)
With doubletails look for one with even lobes, you don't want one with an overlarge bottom or top lobe as I have found that this can cause a couple of problems swimming (I.M.E)
Veiltails are often overlooked for flashier betta's but I try not to make this mistake, veiltails when properly cared for can be beautiful!
I tried not to miss anything out but probably did anyway!
The 2 most important things to me are to know what I am looking for, but to also know that it is not a bad thing to change your mind!!!