The options available can be overwhelming. There are bolt-actions, lever-actions, semi-automatics, pump-actions, and more, and they come in a wide-ranging selection of calibers. The first thing you'll need to do is to consider where you'll be hunting, and what game you will be pursuing.
While I'm no expert on ballistics, I do have experience, both direct and indirect, with what I classify as the "two sides of the debate": Heavy, larger-caliber, relatively slow-moving bullets, and light, small-caliber, high-velocity bullets. Both will, and have, killed deer, and both can do it well. Let's look at which choice may be better for your unique hunting situation.
Location, Location, Location
Here in my native state of Florida, most of our hunting woods are thick, so visibility is usually limited. The average distance that I've identified and killed bucks is 30-40 yards. I have taken Florida deer as close as 10 feet from the base of my tree, and as far away as 115 yards, but the average gives you a pretty good idea of what I've come to expect. We do have areas that offer a large view, such as the multi-acre scars known as clearcuts, but by and large, most of our hunting is done close-in. In view of this, I prefer a heavy, slow bullet in a light, agile carbine. I get the most for my effort; when I have to act quickly, the short, light carbine is easy to handle, and at those close ranges, my 240 grain bullet will deliver a solid, deadly punch. Out of 16 deer and 5 hogs shot with that Ruger.44 semi-auto carbine, none have ever been lost. And as I said, the farthest shot ever taken was 115 yards. Within those bounds, it's a great choice.
Of course, if I were to spot a buck across a clearcut, 200 yards away, I would be more comfortable with something like a 30-06. The reason for this is that, although the 30 caliber bullet's diameter and weight (usually around 150 grains) are both smaller than my pet 44's, it travels at a much higher speed, or velocity. Since it doesn't carry as much "punch", or energy, as the 44, it will carry what it does have farther. Small diameter, high-velocity bullets such as the 30-06, 308, 243, 7mm, 300 Win Mag, etc, are also considered more efficient for the task of penetration (although in a whitetail deer hunting situation, I have shot a 240 grain .44 slug all the way through a buck, end-to-end, so I don't hold to this rule).