I think you have to define a few things. What is "tack driving" to you? And what distances? What is your primary use (hunting, marksmanship, etc)?
Tack driving to some is 1MOA at 100yds, to others it's sub .5 MOA at 1000yds. There is a major cost difference in the two. If you could get a .5MOA gun for $500, everyone would have one. Not saying you have to drop 3K on a good gun, but you have to have reasonable expectations with that budget.
I would answer this that you will get very acceptable quality out of several guns.
2. Stevens (older Savage versions w/o accu-trigger basically)
I recommend these b/c they are all good out of the box rifles and are easy to upgrade as you go. With a minimal investment in some basic tools, you can even change barrels on the Savages/Stevens at home. I build rifles on these all the time (.223, .243, .308, .260, 300WM).
Don't forget the need for a quality optic/base/rings in your equation as well.
But #1 to small groups is proper fundamentals. Fit, repeat-ability and trigger control.
I'm just getting into shotgun hunting so I'm learning lots here, but I've been shooting precision rifle for lots of years, so this is where I can offer some payback of knowledge.