While I know a few folks that hunt Whitetails with a .243, and given proper shot placement and correct ammo, it makes a great deer round. I would suggest upping your selection to a .270, .30-06, or .308. If you are new to deer, it might make a difference, it might not. You'll have many selections in these calibers, and you could consider used to open up an unreal amount of choices.
It's your deal, and I'm not trying to tell you a .243 is not going to produce game, just some other stuff to ponder. For the record, a 20ga is not to bad of a deer gun at close ranges.