Apologies for a second answer... I think the first was wrong because I have now been able to make separate definitions for C-SPC and C-@, as described below.
This works to define C-@ and C-SPC separately:
(global-set-key [?\C-@] 'beginning-of-line)
(global-set-key (kbd "C-SPC") 'end-of-line)
To give credit, I derived the answer from here: Rebind C-space in Emacs
after googling "emacs control space"
(Regarding your question, "what key should I bind this expand-region to?", I ordinarily use C-h C-k and type some key I don't think I use. Then look at the function that that key is bound to by default. If it seems useful to me, I try another key and keep looking. If I feel like I will never use the default definition, I redefine it for my own purposes.)