I'm loading 380 with Hornady 115g XTP hollow point, Berry's 100g plated with the hollow base, and Xtreme 115g plated round nose. In each case, HP38/W231 are giving me the best accuracy and recoil performance in a Colt. You'll have to choose your own powder charge.
In the Colt, I only remove the bell with the seating die, lack of crimp has never set a bullet back in the mag or feed ramp (not much recoil in a 380, is there?). I never trim and it doesn't affect headspace in the chamber. I'm very careful to check chambering, but I find no problem with untrimmed brass.
The 380 case wall tapers toward the mouth, so they split rather easily compared to other pistol calibers. This also yields a 'bulge' when you seat the bullet, but 380 chambers are dimensioned to accomodate the bulge.
jak47: All .355 bullets work in 380 and 9mm Luger. 9x21 and 9x23 and 38ACP and 38 Super also. (They don't work in 9x18 makarov, but you didn't ask that.) For convenience, the light bullets are marketed for 380 because they are more popular for that caliber. If you're using a heavier bullet in 380 (which will be a long bullet) be careful of seating depth due to limited case volume. Use published loads only and follow their minimum overall length.