There's nothing wrong with picking up one of these Mausers when then are cheap. The original workmanship in all cases vastly exeeds anything you can get in reasonably priced (say $500) new rifle. What shape it's in today, well you just have to look it over and see.
The 8mm Mauser cartridge is one of the best. It normally has a little heavier bullet traveling a a little slower than our 30/06 (to generalize) so there is nothing inherently wrong there. American ammo is traditionally underloaded, but fine for any hunting purpose. If you want original loads, you can buy the Czech ammo (cheap) or the German or Swede ammo (pricey).
Since you say he is on a budget, he will be tempted to buy the forigen surplus ammo that is all over the place right now. Make sure he knows that much of this stuff is corrosive and that if he uses this stuff his cleaning practices must be impeciable: you can literally rust the bore over night with this stuff if you are lazy.
As for accuracy, I have never found any way to pick out the rifle that is going to be the tack driver with these. All these rifles are now in the 50-100 year old range, things have happened to them and you just never know how they will shoot until you take them to the range and try them out. Some are gems and some are stinkers, that's all I can say from the accuracy point of view.
All these rifles have rugged military sights on them that do not lend them selves to the very finest target shooting standards, to say the lest. I figure that any of my military sighted Masuers that shoots 2" 5-shot groups at 100 yards is probably a rifle that shoots a lot better than I can actually fire it; it would do lots better with a peep sight or a scope. I would say only a minority realy shoot this good after all these years. Of course, you have to be shooting good ammo to test this.
In short, when these rifles are just in from some foriegn arsenal and being sold by the big retailers for under a $100, they are so cheap for what you really get its almost a shame not to pick one up. It is rather optimistic to expect that its going to shoot like someone's $4,000 beanch rest gun, but it ought to be plenty good enough for hunting deer or having fun at the range.