Buy a basic Savage Mark II and spend the rest on ammo.
That's not a bad choice but I believe I'd buy a Marlin XT-TR instead. Having the ability to load 25 shorts in a bolt action rifle with a tube mag is no bad thing. A person can nail a lot of vermin with a load of rounds like that before they need to reload. They're very solid rifles and accurate too. At least mine is. If I need to make war on a rat infestation for whatever reason I'll be ready. I've never had a rat problem anywhere I've lived but there's always a first time. My neighbor stored a bunch of grain for his cattle in an outbuilding about 20 yards from my outbuilding and I had a few rats move in under my building but my cats cleared those out in short order. Well all but the one they brought into the house to show me. I had to kill that one.