Honestly, it's not too much to say in this discussion that hasn't been beaten to death. If you take a minute to read up on your Cartridges of the World as you move from one round to the next you will soon find that they are all suitable for white tail. From .243 to .300 win mag they will all do the same job. Two questions you should ask yourself.
1. How much recoil do you feel comfortable with?
If you want light recoil lean towards .243 if you want to feel that your the man that took a beating to kill the deer get a .300 win mag. Honestly, it doesn't matter how hard you hit a deer or how big the round is (the 7mm-08 proves that. It's light, small, and devastating) once the vitals are hit the deer will be dead. Period.
2. How much are you willing to spend on a box of shells?
Your gonna buy a box of shells to punch holes in paper at least for the first month or two. Do you want to spend 24.95 + per box (generally the more odd the caliber the more expensive the factory load is) or is a $9.95 box of Remington or Winchester do just fine?
My latest rifle ended up being a 30-06 because of the wide variety of inexpensive ammo available. Also, I don't really feel the recoil of the 30-06 pushing a 150 grain pill. Any caliber in the range I listed before (.243 - .300win mag) will do just fine up to at least 300 yards. Honestly you probably won't have many shots past 200 yards. If you do anticipate past that type of distance regularly then lean towards the .308, 7mm-08, and 7mm they have a slightly flatter trajectory. If not then go to the store and pick out the rifle that feels the best and then get it in the caliber that sounds "fun" to shoot.
Best of luck.