I chose archaeology cause I've always LOVED the idea of digging up fossils and other artifacts :D World of Warcraft introducing the archaeology profession back in the day got me absolutely hooked on it aha, now any time any game has an archaeology feature I'm like -Grabby Hands-
I also very much didn't like the way banking sounded. Having to trade in items to level up the secondary place to put items is... odd? Especially since, as far as I'm aware, your item inventory doesn't exactly have a limit. So it's odd that you'd have to trade stuff in to move them from an infinite storage space to a limited storage space. (Not to mention the whole item-collection aspect of it is.. not at all what I'd think of when I hear the term "banking". I don't think the concept of the profession really fits the name.)
As for ranger, the description sounds neat enough, with it rewarding you for going through the campaign and all, but I think having four different words for types of fighting (Campaign, gauntlet, hunting, and ranger) would get a tad confusing. Especially since the description sounds an awful lot like bounty hunting, and we already have a "Hunting" profession, so I think I'd just mix those two up a lot. I'd still definitely use it if it did win, though, even if I'd prefer archaeology :P