The 686P (or 686+, as it is sometimes called) is a 7-shot, L-frame model. 627 is a larger N-frame and 8-shot as you said. 686 is a little lighter. I have the 686 SSR (6-shot, forged trigger & hammer, factory trigger job, bead blast finish) and it is very nice!
Can't help you much with the alloy revolver question. Generally, the lighter the gun, the more you will feel the recoil. Practice, try some different grips, and practice (yes, I am repeating myself). If you intend to carry, then the 327PD would be a great option, imo.