.223 is cheap and economical to shoot but only good for varmits. Yes some people use it for deer, some people also use .243 for Grizzlies, Not me. The 7.62X39 is an extreamly weak cartridge. Less than a 30-30. A lot of the imported stuff uses corrosive primers also. Quality control is very poor too with the imported stuff. Remember you get what you pay for. Cheap ammo is exactilly that cheap ammo. The adaptors I have seen will be ejected each time you open the action. To me they are more trouble than they are worth.
If you want to hunt deer get a deer gun, one capable of making a clean kill, even if you don't do your part correctly. Keep looking you should be able to find a .357 Handi around, check things like Guns Americia or similer programs. My wife likes to take one of my .35 Whelens and reload some light .357 pistol bullets with a reduced load. Real light recoil and fun to shoot in a large caliber hunting rifle. When I want to shoot something with no recoil I shoot a .22, great practice. We go through two bricks of .22LR a month in this house. The major problem I have with a .223 is wind drift. The slightest breeze will blow it off 6 to 8 inches at 200 yards, it's hard to just hit the paper (12X12) at 300 yards. I carry a .223 during the winter for foxes. It's also great for shooting the heads off Grouse and Ptarmigan at 50 to 100 yards.