Any will do fine on deer.

The 25/06 Rem. , if you did not already know, is essentailly a 30.06 Spr. case necked down to .25 cal. Using a quality 100 to 120 gr. hunting bullet, this is an excellent round for deer. It'll also flat move out light weight varmint bullets. As far as recoil? In my opinion, recoil is not a problem until you get into the 30 cal. so called Magnum rounds. Problem I have recommending the 25.06 Rem. is that it is not a "popular" round. Lots of folks use it alright, but when compared with other deer hunting rounds, it is rather seldom seen. At least where I hunt. For example, in the course of this coming season I will hunt with something like 40-45 different folks. Only 1 uses the 25.06 Rem. This translates into the fact that factory ammo can be iffy to find and you will not find a wide variety of offerings. On the other hand, if you get into hand loading the 25.06 Rem. is a beautiful thing ! You can work up spectacular performing , long range ammo.

My personal favorite is the 308 Win. This short action round is excellent for hunting. I have taken gobs of white tail deer at ranges from about 30 yards to 300 yards, mule deer out to about 325, coyotes to past 400 .... and hogs at 20 feet! Most 308 Win. rifles like 150 to 165 gr. bullets moving at 2600-2800 fps.

Second for me would be the 243 Win. It is an excellent, mild recoil round for deer. It is a round built on the 308 Win. case , necked down to about .25 cal. With 100 gr. hunting bullets, this is a super duper deer killer. And it is an excellent choice for hunting varmints. A 75 gr., rapidly expanding varmint bullet is going to leave a 243 Win. screaming and will drop a coyote farther out than most of us can masterfully shoot.