If they are corded I'm not sure, but if you turn on by the controller, it's been my experience that that controller gets pegged as player 1.

If you turn on at xbox, and you have a wireless and a corded controller, the corded will always get player 1 port

The core system is just to get you started if you don't actually have the extra hundred dollars or so, the problem there isn't really a deal there.

By the time you pick up the hard drive and a wireless controller (both included in the premium) you haven't saved any money, but have actually spent more, and if you were like me and had to get a memory card to get yourself started. 

 Bottom line the premium system is where the deal is, and if you have a fancy HD TV you may want to think about the elite version since it has outputs for the higher end HD displays.