ORIGINAL: wyotimberghost
...if you just started shooting, chances are the .270 will still shoot farther and more accurately than you are currently capable of shooting. Just something to keep in mind. Not saying you're a bad shooter- just saying you may want to practice before worrying about getting a long range rifle. Also, getting as close as you can is a lot more fun than shooting at a speck for most people.
I will second this what wyotimberghost said. Everyone wants a gun that will kill deer from a mile away (so to speak), but in reality, most of us (me included) have no business shooting at any game past 150-200 yards at the most. I have been shooting all my life and hunting deer for 25 years, but my "confort zone" is 100 yards+/-. I have killed well over 100 deer in my years of hunting and even a few out to 300 yards, but for me to take a shot at a deer past 150 yards, the conditions have to be near perfect.
For you as a new shooter/hunter, find a gun that fits you in a mild recoiling caliber such as 308 or 270 and practice, practice, practice. When you get some experience, if you are still hung up on "long range" shooting, you can look into a larger caliber such as 7mm magnum or 300 magnum.
Congrats on your first deer!