Yup. Wireless trading (with people in the same room) can be done almost as soon as you receive the Pokedex. You'll have to play a bit before you unlock WiFi trading, though.
Also know that people can trade you National Dex Pokemon even if you don't have the National Dex.
EDIT: I wouldn't recommend any of the other games. Unless you like throwing your DS at a wall out of sheer rage, Mystery Dungeon is a bad choice. And Ranger just looks stupid.