The SPS Tactical is a good starting point. Before I got into shooting bolt actions, I asked around and the consensus was that the 700 was the best way to go. The Model 7, does have its advantages, if those advantages are what you are looking for. For punching holes in paper for accuracy, you'll want a 700 short action.
A little correction of the above post which states that the SPS has a stock with a full bedding block. The stock is a Hogue stock that is pillar bedded. It does NOT have a bedding block. All of the ones that I've seen and shot were very accurate. It's a pretty popular rifle at the range where I shoot. It is accurate, has a heavy barrel and has that whole tactical look and feel going for it, at a budget price.
It has enough heft to it to give it that steady feel when you're shooting off of a bench and it isn't so heavy that you can't hump it around in the woods a bit, if you are so inclined. The downside to it is that the finish sucks. If you don't wipe it down with oil after every outing, it will rust. Once I got mine where I wanted it, I just Duracoated the whole thing.
I'm relatively new to the bolt action scene. I can't speak from experience going back 20 years. I've read lots of post from guys that can speak from experience going back 20 years, and there is much discussion about accuracy and improving it on the rifles that they have messed with.
Being new to bolt actions and precision shooting, I'm only familiar with mostly rifles of current production; and from what I can tell, getting a rifle that will shoot minute of angle or better isn't that hard these days.
If budget is a real concern, I'd start beating the bushes for an ADL and then upgrade as finances allow. If you can swing the SPS Tactical, all you'll really NEED is a scope. Mine punched a bunch of .2 and .3" holes for five rounds at 100 yards, in stock form.
