You aren't planning to hunt - you are looking for a bolt action range toy to kill paper and steel, and want to be economical in your choice.
That, to me, says a bolt action 223 with a 1:9 or faster twist barrel...not much gets more economical.
A Savage 12FV, for example, will push 75gr HPBT/77gr SMK to around 2850fps with the "ole standard" 24.0gr Varget while providing sub-MOA accuracy, and will shoot 75gr Hornady Steel Match to MOA or better. I used to have one and it was fairly easy to make hits on 8" steel at 650yd with the Steel Match ammo, and with 75gr HPBT handloads it was sub-half MOA @ 200yd.
This might be the best bolt .223 out there for target and plinking: Savage Arms
Single shot, left port.
Available in 1:9 and 1:7 twists so you can shoot the really heavy (higher BC) .223 rounds if you want.
Get the 1:7 and a couple boxes of Federal Gold Medal with 77gr SMKs. This should be half MOA or better.
If I was a .223 guy (which I'm not, but I'm willing to be), then this Savage LRPV is the very first bolt gun $$ I would spend.