Everyone will tell you that what they ride is the best. Seems those that use Speedplay love them, those that use Look or SPD-SL love them. You probably can't go wrong with any but you may find you like one type better. Looking for lots of float then you probably want Speedplay. Want a larger platform then Look or SPD-SL is probably the ticket (though the Speedplay folks will tell you the cleat or a stiff sole shoe makes up for the platform but I'm not sold). Fwiw, I just stared using some Ultegra SPD-SL pedals (I'm fat ^^) and while I'm still struggling to clip in, they are great once I'm moving. Clipping out is a bit tight but not problematic.

As for different types for different purposes I think the main distinction would be road or mtb (which shed mud better and are easier to clip in and out - in general) but I was using mtb pedals on my road bike so it's not a hard and fast rule or anything.