You already got a lot of imput, but I'll give you my .02.
In a short action:
* 7mm-08, will do all you want to do. Has hunting bullets close to 120 for the deer you have. Also gives you options if game gets toucher. Hogs with a 150+ bullet. Elk as well.
* 6.5 of some sort, great round. I prefer the 6.5 Creedmoor(own one), but the 260 Rem is the other common one. With Norma coming out with brass and ammo for the Creedmoor, I give it the nod. Good choices of 120-130gr hunting bullets.
* 243, is always a viable option, will not get you up to 120gr bullets. But kills many deer every year.
There are others, but have to stop somewhere. 257 Roberts +P or 308 could make honorable mention. I've hunted for a decade with the 257. Bought a 7mm and have never hunted with the "Bob" again.
If your willing to go to the effort to change bolt face. The 270 WSM is a great hunting round(son uses one). I like the 7mm as well, but not as common. (I hunt with a 7MM SAUM).
Good luck getting through all these posts, and post pics of your rifle when you are done.