James - if you have the intended bullets in hand or know their OALs, you can plug the numbers in here and see what different twist rates will buy you in terms of stability in various conditions:
Our newly updated Twist Rate Stability Calculator not only tells you what your SG is, but it also lets you know if you are reaching your optimized BC.
bergerbullets.com
I would suggest a minimum gyroscopic stability coefficient (Sg) of maybe 1.3, although somewhere in the 1.4-1.5 range would be better. These numbers aren't written in stone, meaning the bullet won't suddenly fall out of the sky at an Sg slightly under 1.3, nor will they spin apart at an Sg of slightly greater than 1.5. However, you really don't want to go below about 1.1 or so, because bullet stability will become a major issue. The key is to match the barrel twist rate of the barrel with the bullet at its expected velocity so as to obtain the full intrinsic BC; i.e. "performance" of the bullet. According to Bryan Litz, this occurs at Sg values of 1.5 or greater. Nonetheless, I've shot a lot of bullets at Sg values in the upper 1.3s to low 1.4s and they worked just fine, even though I probably wasn't getting the full BC of the bullet.
FWIW - I've run Berger's 200.20X bullet out of an 03' Springfield with a 24" 10-twist barrel at around 2500-2550 fps and it shot very well. I've shot the same bullet out of an F-TR rifle with a 30" 11-twist barrel at approximately 2650 fps, and it also shot very well. However, the difference in twist rates between the two barrels was compensated to some extent by the extra 100 fps velocity obtained with the longer 30" 11-twist barrel. At 2500-2550 fps, an 11-twist barrel may be a bit slow for the 200.20X bullet, generating Sg values of less than 1.3 in cooler temps and/or at low elevation. The lengths of the actual 200-220 gr bullets you intend to use will affect the outputs, so having those values will be helpful for using the Twist Rate Calculator.
I'd go with a 1:10 twist as others have also suggested, but if all you have is an 11-twist barrel, you could still try it and see whether it was fully stabilizing the bullets. If you observe slightly oval or oblong holes in the target, the twist rate is insufficient. In that event, something in the 185 gr range would probably be a better way to go.