Others will chime in with suggestions...here are mine:
A Ruger 10/22 for rabbits, squirrels - you should use your shotgun if the area you hunt has thick cover or if it is unsafe to use a rifle. Put a 2x scope on it, or iron sights.
For turkey, something like a .17HMR with a 4x scope. Or a 'turkey choked' shotgun for tightly patterned head shots. The semi-auto shotguns are popular for turkey around here, even though we have open terrain.
For deer, you could look for a nice used Savage lever chambered in 250 Savage, which is a classic retro piece from the 60s. There's lots of good bolt rifles out there, new and used.
For example, I had a close look last week at the new-this-year Savage Axis package which includes a basic 3x9 Bushnell. Lots of value in that package, a good build that I figure would not disappoint a young hunter looking for change.
You can get the Axis in stainless or blued bead-blasted. Has the excellent Savage action. Good detachable box mag. Good recoil pad. Metal trigger guard and sling studs. Standard trigger but with a very clean crisp release. Decent plastic stock. Bedded action iirc. The Axis is available in .223, .22-250, .243, .25-06, 270 Win, 7mm-08, .308, .30-06.
If you are used to a .30-30 and a 12 gauge, you will find the 7-08, the 25-06, the 243 to be good deer rounds, with recoil that is well within your comfort zone.
I'd be tempted by the .243 as it is an accurate flat shooter, has super mild recoil, is devastating on deer and fun on groundhogs/prairie dogs/coyotes, relatively cheap to reload so you can practice a lot with it.
Have fun.