If your state allows .22 cf's it'll likely be a handloading situation for proper bullets to handle deer,,,jmo.
Otherwise the .243 will do you just fine with light recoil. The mention .260 and 7-08 are good ones also. Or there's the option of specialty pistols such as the TC's . With practice they will hold there own with some rifles.
In case the later interest you,, http://www.biggamehunt.net/node/25095
243, 260, 7mm-08 all good rounds for deer and will kill out 300 yards if you do your part. If your shouder is real bad, you should stick with the 243 or 260. I perfer the 260 because it has good bullet weight (120gr-140gr), high section densty and high BC.
Hey, look into the 6.8 SPC cartridge. I have one in a Stag ARMS AR-15 and it performs wonderfully out to 300 yards and it has less recoil than the .243 Win. It shoots a 270 cal bullet and I shoot a 110 grain Sierra Pro Hunter bullet from Silver State Armory. I believe remington and ruger and T/C chamber it along with many of the "black guns" like Stag arms and DPMS. I used this cartridge on a large doe in MN this fall at over 300 yards and she was toast after a thru and thru front shoulder shot. Great knockdown and very little meat damage. Look into it, It is a fun, short, light recoil caliber.
One of the things I struggle with when afield is keeping my rifle clean and in good working order. Small amounts of dust and dirt collect moisture; moisture can freeze rendering your action immovable when you need it most. I have seen this happen on multiple occasions, and over time, I’ve learned the cause and how to prevent this from happening.
The first thing that you need to avoid before going afield is leaving excess oil on the gun. Oil will trap dirt and sand in all the wrong places....