I'll second Steel_Talon's advice about the .30-06. Anything that's been bringing down big game for a century must have something going for it. Ammunition is cheap, plentiful, and has enough varieties to adapt to your game.
As someone who took up big-game hunting as an adult (mid-40's when I started), hunter safety is an important first step, but I cannot overstress the suggestion that you find someone to mentor you.
I had the help of several people to teach me a lot, and there's a lot to learn. Unfortunately, some of the first people I met were pretty worthless as mentors (they resented things I didn't know--I was ignorant, not stupid), but once I got connected to a couple of helpful guys, I had a lot more fun, not to mention success.
I'll probably never be a great outdoorsman, but I'm at the point where I can go on a hunt, have a safe and good time, make a clean kill, and enjoy eating what I shoot. That'll do.