Re: AR-15 with 1/12 twist barrel
The M193 isn't what you should use, it's just what the military did use as standard ball ammo for the M16 and M16A1 rifles. Lots of much better options out there, and almost all will beat the pants off the M193 in terms of accuracy. Most of the FMJ Ball stuff is about 2-3 MOA, or a bit better if it's a real good lot. Crappy stuff, but suitable for combat accuracy.
The M855 is the longer 62 grain bullet, same as the SS109 NATO round, and needs a significantly faster twist to be properly stabilized. Out of your rifle, they'd tumble, keyhole and give horrible accuracy. Not dangerous to you or the gun, just won't be able to hit anything with these.
Long450 gave you some good advice here, both in terms of bullet weight and powder choices. Try H335, H332, 748, N133 or N135 with bullets in the 45-60 grain range, and you'll get your best accuracy and decent velocity. Need the slower powders like RL-15, Varget of N140 when you get to the heavier bullets (69-82 grains), but your twist makes these a non-issue. Stick to the faster powders and you're good to go.