looking at barnes load data
For a .22-250 with a 24" 1:14 twist barrel the fastest load they list is a 36gr varmint grenade loaded with 40gr of RL 15 powder. It flies at 4417 fps.
As to the twist rate you would want moving 600fps faster, Just going out on a limb at 1:15 or 1:16. Do not know with certainty though.
Its going to burn barrels so fast that if you weren't happy with the twist rate you would get a chance to try something else pretty quickly.