Well, since you’ve got your own domain, you can use lots of different addresses – like consulting@firstlast.com for your consulting business, and me@firstlast.com for your self, etc. These can all go to the same mailbox if need be . . .
Sure, though I’d limit it to as few different inboxes or aliases as necessary. “Contact” and “email” sound a bit redundant as they stand for more or less the same thing - general contact. I’d consider more diverse names, like “help”, “quote”, “billing”, for different purposes, as long as they make sense. Though you originally asked what you should use as the primary, which I’d guess would be most general.
One thing about “email” I don’t like is that it’s redundant by itself, i.e. it points out the obvious - we already know it’s an email.
Overall it’s really a matter of personal preference.