What do I need to bring the game up to date, and what mode is most populated? or popular?
You don't need to do anything. If you have BC2 on Steam or Origin, then you will have the latest version and you can simply launch the game and look at the server browser.
I'm not sure what game-mode is most popular, but Rush was definitely the most fun when I played it. It's much more interesting and exciting than boring old Conquest mode. Plus, in BC2 the maps are actually designed really well for Rush, unlike BF3 where it's more of an after-thought.
Unfortunately the Vietnam expansion is pretty much dead, but there should be plenty of people playing the vanilla game. Bad Company 2 was the last Battlefield game that avoided releasing multiple paid DLC so it didn't fragment the player-base, which IMO is a sin.