OK, if you want a battle rifle and need to mask its purpose from your SO by saying its a hunting rifle, get the PTR-91. I had a HK-91 in the late 70's. As reliable as an anvil, more than reasonably accurate, but very heavy, a terrible trigger, and a very high scope mounting requirement that prevented a good cheek weld. I still have an AR and a Garand. If you want a semi-auto battle rifle, get a semi-auto battle rifle. No excuse is needed.
The other two are actually sporters. For its price, the Steyr should be GTG out of the box. I prefer the design of the CZ, but it is built to a price point and is not going to be as slick and smooth feeding out of the box. However, a good gunsmith familiar with tuning Mauser style actions should be able to make it plenty slick for a couple of hundred $. You can always live with the CZ at first and have it tuned later.
If you have to squeeze your budget, scrimp on the rifle - not on the glass. See if you can find a good deal on at least Leupold VX3 or equivelent glass. Their 2.5-8x is a good general purpose scope. If money is tight, consider finding a deal on a good used scope.
.308 is MUCH more available than the other cartridges you mentioned. But the others are better balanced for sub-350lb game like white tails, mule deer, or antelope. If you want a lighter, flatter shooting caliber, but want something you can find in even the smallest town, consider the .270 Winchester. Of course, in no way is a 150gr Nosler AccuBond in a .308 a bad choice for these animals.
