[Baron Munchausen]

Mines already skip shields, so any of the shield skipping damage types would be a waste. The others must work fine, because there was a change to the game a few updates back that made mines not attack if ships did not contain anything they could damage. Engine destroying mines are a very evil, now. You can place a minefield of engine destroying mines at a warp point with your other defenses and the enemy appears as usual -- with no engines! -- and you mop them up.

The only other types that would be generally useful on mines would be 'only weapons' and 'only shield generators'. But some of the more exotic ones might be useful in special situations. Only Master Computers for example, would be horrendous against the AI in the current patch. It is now hard-coded to always use the MC when it has been acquired. The Increase/Disrupt Reload types from Psychic/Crystalline might be interesting in warp point defense, too. It's all a question of how much typing you are willing to do to setup all those special warhead types.