I own a 360sc. I practice with Remington or Winchester 130gr FMJ, whichever is cheaper. I carry Federal 125gr Low recoil. Its not as much power as the +p, but very controllable. I tried the Speer 38+p Golddots - really did some damage to the backplate - left some indents. In my experience, the 360Sc won't hold up to a lot of practice. The titanium cylinder wears out quickly. Your miliage may vary.
I now most often carry the M&P 360, which has a steel cylinder.