Some games need the hard drive to run.
As for game saves these vary from game to game Oblivion - which will run on a core system - uses 2mb a save.
You can get a core and add the other bits later but this will cost you more.
I agree with Phantaxus. Even if you only want to play games offline, the extra cost for the premium over the core system is easily worth it - you'll end up paying more in add ons later on, and as above, some games require you to have the harddrive to save progress.