Go with the 22-250. It's a better round for what you want.
I personally don't look at cost as an issue. For the type of shooting you want to do and practice for one doesn't sit down and shot boxes and boxes.
Buy the Tikka or any other good bolt. With hornady or federal ammo they'll give you under 1" groups and even with good glass the outfit will run under $900 and probably under 800. Last I looked a National Match AR is going to run more than that.