I agree that 243 or 308 would be a better general purpose caliber. With a budget of 800 if you shop smart and don't need top of the line you could put together a hunting rifle in the above calibers or something similar, and set up a 22 for practicing.
A good point was raised above about the cost of 223 practice ammo vs 223 hunting ammo, something to consider.
If you go with a 308 you can at least get FMJ ammo which tends to be cheaper 60 cents or so.
I have a marlin 22 bolt action they run around 160 new and i threw an old redfield scope on it. If you shop used and get an old redfield or weaver thats 200 leaving you 6 to put together a hunting rifle. Grab an axis or similar class rifle for 3 or so and put the rest into a redfield revolution, nikon prostaff, or various leupolds available.
A good point was raised above about the cost of 223 practice ammo vs 223 hunting ammo, something to consider.
If you go with a 308 you can at least get FMJ ammo which tends to be cheaper 60 cents or so.
I have a marlin 22 bolt action they run around 160 new and i threw an old redfield scope on it. If you shop used and get an old redfield or weaver thats 200 leaving you 6 to put together a hunting rifle. Grab an axis or similar class rifle for 3 or so and put the rest into a redfield revolution, nikon prostaff, or various leupolds available.