Nobody mentioned the 1917 Enfield in .30-06? It's got a good receiver aperture sight if you're not planning on scoping the rifle. The 98 Mauser is the gold standard in sporterized military rifles, but I'd take the 1917 over it if you don't plan on alterations. Of course, everything is made for the 98 Mauser.
I built a cheap hunting rifle out of a Spanish Mauser 93. It was in 7x57, a very good caliber, but the rapid rifling rate would only really work well with 175 grain round nose. I tried 140s and 150s in it and they didn't shoot well at all. It was about a 2moa gun with 175 grain Hornady round nose. I forget what powder I used, in my notes somewhere. I'm thinking IMR4350, but don't remember for sure. It made for a decent short range (250yds or less) knock around gun and I didn't have much money in it. The rifle cost me $60, I think. It was a short, handy rifle, too, though a bit heavy like any mil surp.
There is a "Siamese Mauser" that has a large enough head size to its original chambering (can't remember the chambering) that they are often rebarreled for .45-70 and are strong, can be loaded really hot. A guy tried to sell me one, once, in .45-70, but he wanted $500 for it and I didn't need it $500 worth of need. Besides, I don't know if the thing shot well and I'm not going to spend that kind of cash on any sporterized mil surp unless I shoot it. I'm sure he had a lot of money in it considering the cost of a barrel and custom building the thing, though. If we had T. Rex hunting in Texas, I might have bought it, LOL!