Th issue you may run into with a Mauser, is they can get expensive very quickly. Even the pre-bubba'd model from the pawn shop for $100 can end up costing well in excess of $250. I have found many times that a rifle is cheap for a reason, usually due to issues that require a bit of cash to fix. There are other things that often need attention before they are truly suitable for hunting as well. For starters, the two-stage trigger is not near ideal for a hunting rifle and should be replaced. And just that will likely be $80 at minimum, eating a large chunk of your budget. And that's not even beginning to get into the safety or stock work, or any machining that may need to be done.
Basically, unless the rifle is ready to go as purchased, Mausers will often end up being expensive projects to set-up properly. There are better choices for a low-cost hunting rifle that will also perform better and be safer than a hacked up Mauser.
My suggestion is to look to a Stevens or Savage for a low cost, yet very accurate, safe and reliable hunting rifle. They can be had for little money and often in good shape. They are easily worked on by most anyone and have a ton of affordable aftermarket parts available.
I only relay this information as I had looked into doing something very similar with a Mauser I already have, and found it would be very costly to "modernize" the rifle, or even to just bring it up to pace with a decent commercial rifle, like a Savage. Just because they can be purchased for short money doesn't mean they can be converted for short money or even restored for short money. Mausers are often money pits unless you buy one to be used as purchased.
If you do want an old surplus rifle to work with, look into finding a Mosin Nagant M44 with a good bore, or even a 91/30 with a good bore. They use a very capable round, are a very simple design, and don't need much of the work that a Mauser will to be turned into decent hunting rifle. You can basically just swap it into a sporter stock, add one of the scope mount and bolt handle kits and slap a scope on it and have a decent rig for very short money. The triggers can also be improved with a bit of work as well. I myself have several Mosins, as well as one that has been sporterized in a manner similar to what I described. It shoots well and has even taken a deer. I have exactly $280 in it including optics and it will shoot inside 2" at 100yds with soft point ammo. Not bad for money invested and better than I could get from a Mauser with a similar investment. It does have one issue though, and that's the safety, as it is hard to operate, but once it's on is very secure. I just don't keep a round in the chamber until I want to fire, it solves that easily. But you can make them a bit easier to operate, and they are quite safe once engaged. But for a low cost sporter, they are a decent option. If you do a google search, you can see plenty of Mosin projects done by others. Timney also makes a trigger for them as does Huber Concepts, and both are under $100.
If you really want to get involved with a Mauser, than you are more than welcome to. I am not saying "don't do it", only stating the issues and that other options can be had for less money and often easier as well.
I would opt for a Savage/Stevens or a Mosin myself. And that's after building both a Stevens bench rig and a Mosin sporter, and owning both a Savage I bought in .243 used for short money, as well as a new Stevens in .308. I also have the earlier mentioned sporter Mauser in 25/06, and though it does shoot, it would take a good investment and a bit of machining time to bring it up to the level my other rifles are on.
Whatever you do, good luck with it. I hope it turns out well and you have a nice rifle in the end.
Kenny