Single MM vs. Double P vs. PJ

A Stingray pickup and preamp would be my choice. It has a character of sound that's ideal for those styles you mention. Having in the sweet spot also makes the Stingray pickup sound what it is.

 

Overdrive screams MM!!!

 

I'd go PJ. The P will have more bottom than the Musicman and will have more low mids. Bring in the J pickup for some mid cut but extra high end to distort. Back off of the P pickup for grinding treble.

Double P is another bold choice, which I approve! Just not sure because I haven't had one in a 5.

Passive basses just plain work better with dirt pedals. Of course, in my humble opinion.

 

I have a double p and a MM spector the 2P is much fatter and fuller than the MM witch gives it a huge punch with tons of low mids,.. the MM (nordstrand bigman) is still fat and punchy but more high mids with a tighter sound and brighter highs like you'd expect from a single pickup, for metal id highly recommend the bigman , im getting ready to order a custom spector build with a Nordstrand bigman and a NJ4SE jazz pickup in the neck position to add some fatness when needed

 

I saw metal and I assumed 5. When my band drops to D I bring my low B down to A. It is killer having 2 sets of open octaves. Feel free to play the hell out of a 4 though!

Playing with pickup heights you can dial a PJ to sound a lot like a MM, can't go the other way. Also I can't help but feel that the open airy sound of a single coil would be better for a bridge pickup than the mid forward series P pickup sound.