Ruger American Rifle with a Nikon ProStaff 4-12x40mm Riflescope, Matte w/ BDC Reticle?

So I was wondering if that is a good combination, since that will be my first rifle and I don't have alot of money. And by the way I'm getting 30-06 caliber.

Well Ruger makes a great rifle and Nikon makes a good scope so it sounds like a god combo to me.

Fine combo, but do you need a 4-12x? That's a good bit of power. You can do the job with a 3-9x for almost any hunting other than hunting on the plains.

From handling the Ruger, it feels solid, the bolt and trigger are crisp and there are a lot of features on the rifle I like. It compares favorably with a Tikka T3 or T/C Venture. I shoot Browning A-Bolts which is why I like the tang safety and short bolt throw. 30-06 is what I've been shooting since 1974 so can't fault the cartridge. I like Nikon products but I'm not a fan of the BDC scopes, yes they can work if you know how to adapt the tree to your bullet performance but it puts a lot of info in front of your eyes while hunting. I prefer the more simple NikoPlex reticle. You can sight in to have a 200 yard ZERO, which I do recommend;it just means 2 inches high at 100 yards and the change in POI isn't enough to worry about in a hunting situation.
This doesn't sound like a factory combo which often use a bottom shelf scope, think you will be fine.