Look at Hunting Rifles Forum...A member here has organized a Tikka .22-250 with a 1 in 8 twist at a price under your budget, just for 24HCF members.
That would be hard to beat.
My 8 twist .22-250 Shilen/Mohawk loves 75's and 80's, actually groups 80's slightly tighter than 75's.
8 twist will handle about any bullet you want to feed it, from varmints to WT's and hogs.
DF