I recently bought White 2 used, and the previous owner had made it to the Elite Four. Other than the starter, are there any Pokemon they might have chosen over another (and so I should attempt to trade that to another player and then trade back once I start anew)? A similar scenario would be the Mount Moon fossils in Red and Blue; one can only get both in the same playthrough via trading with another player.
Your starter and your Fossil Pokémon
As you mentioned, and like most other games in the Pokémon franchise, you only receive one of the three starter Pokémon in a playthrough without trading, which is selected at the beginning of the game.
Generation 5 also has a pair of fossils, of which you can only select one during a particular playthrough of the game. Selecting the Cover Fossil will get you Tirtouga, while the Plume Fossil will get you Archen. In Black/White 2, you receive your fossil from Lenora in the Nacrene Museum, while in the original Black/White, you receive your fossil from a Backpacker in the Relic Castle.
Both versions of the game also have a set of version-exclusive Pokémon, but which of these you have access to is, of course, determined by which version of the game you have, rather than choices you make during the game.