just my opinion! .243win is the smallest caliber I would ever hunt deer with. that said I have several buddies that hunt deer in Tx with .222rem. they take neck shots to drop em quick because of all the thorny brush.
My son's .243win is a Ruger American Compact.All things considered it is a decent rifle. They "borrowed" heavily from Savage with there trigger and barrel nut. The trigger is not as clean as the savage Accutrigger at least not the one I have, but It is better then most of the factory triggers I have pulled from similarly priced rifles. With the short 16" barrel the best groups I got with factory ammo was 1.5" @100yards. Was just this week able to get .85" @100yards with handloads.
I knew a guy in SC that hunted with nothing but a 22-250. Upper neck and head shots though. With the new and improved bullets on the market these days and burning down range at 4000 fps I would say it would be ok as long has you don't impact leg bone that would alter the bullets path into the vitals. My $0.02
If it's for a recoil sensitive adult or child (wether medical or mental) I'd say go for it, but go for lung/heart shots. I'd shoot Nosler Partitions out of it. Many, many deer have been killed in Texas with .22 centerfire bullets.
However, if it's for a non-recoil sensitive person then I'd start at .243 as my minimum. I have a 6mm Remington and like it really well on deer.
Edit to add: I own a Savage Model 12 FVSS in .22-250 that I've often considered taking deer hunting but never have as I also own a 6mm Rem., .270 Win., and a 30-30 Win. The later three get the nod for deer.
While a world of deer have been killed by .22 cal centerfire rifles, my personal experience, and my family's has been that the .243 with a 95gr or 100gr Nosler Partition will result in a higher percentage of one shot DRT's with minimal drama. Again, just my experience...
In the hands of an experienced shooter with the right bullet it might be ok. I too have a Savage FVSS in 22-250 and at some point will try it on deer. Last year I bought a Savage model 16 in 260 Remington for a lighter recoiling rifle than my old 30-06. After having shoulder surgery I can't take the kick like I used to. IMO a kid or woman could shoot the 260 without any issues.
I know it's not a 22-250, but in the same ballpark. My wife used a .223 AR last year to take her first deer. Recoil was an issue as well as the stock length itself. I coached her heavily before season on bullet placement and waiting for the right shot. Shot was just behind and above the shoulder. 62 grain core-lokt through both lungs, 63 yard shot, 20 yard recovery. Zero meat loss and deer was down in seconds. I think putting the smaller bullets like that into the shoulder would probably result in lost deer but staying away from heavy bone and drilling both lungs seems to work great with a smaller caliber. I own a Howa Predator rifle in 22-250, they're wicked little guns for varmints and I have no doubt I could take a deer with a suitable bullet. Just have to be picky about the shot.
I have seen deer taken cleanly with neck shots with a 22-250. But like some others have pointed out, I feel like the 243 is a bare minimum. It is also a more universal round. You can use 55gr bullets and get all but identical performance of the 22-250. Or go with 95-100gr bullets and kill any deer around with minimal recoil. All 3 of my kids started with my 243 and my 11 year old son has hunted with it and killed deer since he was 7. I'd go with the 243.