For plinking, if you don't reload, you can get the 7.62 rounds for cheaper than .308 rounds. I've seen the 7.62x54R rounds for about ten cents a piece. (Look through southern ohio gun, they usually have good deals)
If you do choose to reload, and want to think about hunting with the gun, then the .308 is the way to go. There is more ammo availability for the .308 factory, and also cheaper brass available for reloading. Brass for the 7.62 is expensive.
So if you are planning on buying surplus ammo and plinking cheap - the 7.62, and if you are planning on hunting with it, and possibly reloading - the .308.