Flat Tire,
Kraig gave you the Greenhill formula for bullet stability. Notice that what matters to it is bullet length. Weight and velocity don't even enter into that simple equation. So your question should have asked what bullet length is best? Weight, especially at long range, also matters because it affects ballistic coefficient (BC). So figure optimal stability will give you best accuracy in dead still air and BC will tell you which bullet is least affected by wind at 500 yards? You really need a combination of the two for long range, so I would suggest you pick the bullet with the highest BC number that is still stabilized well in your gun.
Most bullet makers don't publish that length number. You have to measure it or to guess it from a photo. This is not to say weight has nothing to do with stability—it does; so does velocity and air density, which are also missing from the Greenhill formula—it is just that they are not as significant to stability as length.
So, then, how do you decide you have acceptable stability for a given bullet? There is a more modern, complicated and expanded version of the Greenhill formula worked out by Don Miller that was published a few years ago. It does take velocity, bullet weight, and also temperature and barometric pressure (for air density) into account. It is too complicated to write out here, but if you have Excel or the Calc spreadsheet program in the free
Open Office Suite, you can use either open an Excel file I made that does the calculations for you. You just fill in the blanks. It is called the Bullet stability and twist estimator. You can download it free from my public file repository
here. It will tell you the best twist for an entered stability factor (1.4 to 1.5 are considered ideal by a couple of good sources, so I use 1.45 myself) and it also tells you the stability factor you get with your existing twist. Just enter the numbers.