If this is your first hunt, I'd probably recommend a rifle. Either the 7.62x39 or the 308 Win will work very well for the range you describe. Make sure you match the bullet to the game. Stay away from FMJ's and get a suitable soft point.
For the 308 Win, most standard 150 grain soft points will be fine. No matter the caliber you choose, shot placement is king! Practice with your chosen combination and use that for your hunt. Good advice on the sighting in. You have to know where its going to hit and be comfortable with it. Whether you choose your pistol or go to a rifle, I recommend practicing on a paper plate or whatever with a 4 inch circle drawn on it. Your max range will be the distance you can keep all your shots within that circle.
The kill zone on a deer is a bit larger, but trust me, if you are going to be walking the woods, you're going to be bit tired and the shot may be a quick one. Combine that with the energy release you'll have when Mr Bucky shows out of nowhere, you'll find the amount and kind of practicing you do will pay off.