If you are new to shooting you should avoid magnums as the extra smoke and ruckus doesn't get you that much more range.
The list of great new hunter cartridges is long, mine looks like this: 30 30, 270, 280, 308, 3006, 7x57, 8x57 to name a few. These are milder kickers that will take all the game you have mentioned.
I personally am a fan of 3006 due to it's unique combination of power, versatility, availability, and economy - but all of the above would be fine.
As far as rifles, well, you need to go out to a well stocked sporting goods store and handle a Remington 700, a Winchester Model 70, a CZ 550, a Ruger 77 mk II, and probably a Tika. One or more will feel "right" to you.
My observations are that Remington quality (yes in the hallowed 700's) is off and the trigger sucks. CZ's are well made but a little bulkier. Winchester's are well made and I think an excellent value these days. The Tika's are fine and shoot well although I don't care for plastic parts on a rifle.