There are several threads on this very topic you can read, but I'd suggest checking out a few things:
First, get some Trailboss powder and load your own cartridges. With Trailboss, you can take a traditional high-recoil cartridge and totally tame it. It likely won't be good for hunting, but will get a new or recoil-sensitive shooter up to snuff on whatever rifle in any chambering. Increase your handloads with the powder/bullet combo that meets your minimum requirements for deer and you're there. All the traditional cartridges like .270, .30-06, .35 Remington, etc. can be tamed by handloading. So pick a rifle/cartridge combination on other criteria.
For some neat deer cartridges that are on the lighter-recoil end, look at a number of the built-for-AR15 cartridges that also go into bolt-actions etc. Like .300 Blackout, .450 Bushmaster, and my favorite, 6.5mm Grendel. These are all lighter-recoiling than the more traditional .243 and yet still effective on deer.
Also check out 6.0mm Creedmoor as an alternative to .243. And, because it's popular and there's tons of rifles at your LGS's in 6.5 Creedmoor, consider you can handload it down to whatever level you want (with the right powder) to be effective at your purpose.