You can finish each of the games easily on their own.
However, a lot of the skill builds that are 'favoured' by players and peers are mix & matched between the different campains, so in the end you'll want to get all the games for their skills and whatnot. This is certainly the case when you go play PVP.
A good starter would be to obtain the GW platinum pack (prophecies + eye of the north) and when you feel the need to expand, get the other two chapters. All depends on the way you eventually like/play the game.
Hope this helps
