You can get Mausers, Mosin Nagants, Enfields, etc. for $60-$200 depending on the quality. Seriously, the surplus WW2 rifles are dirt cheap and most are very accurate and powerful. I myself have a Mosin Nagant that I got for $100, but I don't hunt. As mentioned before, the SKS is a very option for a semi-automatic, as you can get them for dirt cheap. Bottom line, get a cheap surplus gun and if you screw it up, buy another one.
Rsk, where do you live? Do you live in Canada or the U.S.? If you live in Canada there are some places you can look for info as to what some people use. For example, I'm thinking of using a bubba'ed p14 and a stock Mosin. I also know of numerous Canadians who use old enfields and other sporterized military rifles for hunting. One thing to consider is what the rifle is chambered for. What it is chambered in, the availability of hunting ammunition will determine what would be a good rifle to use. Another thing that is relevant in Canada is what classification the rifle is in. All bolt action milsurp rifles will fall into the non-restricted class which will allow you to hunt with them. Some rifles like the AR10 fall into the restricted class which means that you can't take them hunting. Finally, some rifles like the G3, the CETME, the FAL, and a few others fall into the prohibited class which means there is no bloody way you'll be able to buy one at all. Btw, it is recommended that if hunting with the Garand you stay with bullet weights less than 168 grains in order not to put too much stress on the rifle itself.
Any of the choices I have seen posted are good. Keep in mind if you stay with a bolt gun, you can hunt virtually anywhere with it that allows rifle hunting. I like the mauser (I have several) and the Moisin Nagant, especially if you handload. I will post pics of a couple of the Mausers I have built if I ever join the 21st century and buy a digi cam. It looks like the one you have in the pic would be a good choice. There are considerably more 7.92 reloading components than there used to be. Most commercial 7.92 tends to be a bit squibby in my opinion since manufacturers are afraid of liability issues if somebody were to stuff this ammo in an old commission mauser. It looks like you would be well suited to get some rise on your stock by making a cheek rest. Unless, of course, that is an original sniper; if you screw with it, I would have to hunt you down and hurt you out of principle.