I know several higly productive deer hunters in AL who swear by the .243 for deer.
Something to think about though is flexibility. A .270 may give you some more options for size and range of game. I've never shot an elk, but I know many have been felled by a .270
OR...you could go the maximum fun option...a rifle in each caliber you wanted to shoot.
You can go as big as you like, BUT...A friend came down with an acute case of "gotta get a magnum-osis" for his first rifle. After ruining a good share of venison with his 300 ultra mag, he's looking at a .257 Roberts now.
Some guys like the wildcat rounds. Cool, but finding ammo is tough sometimes. I like that I can go just about anywhere and find .270 or 30-06 ammo.