straight into the amp on its own might not be the ideal sound for what you’re after, but it’s a good amp. You might find that for a more metal tone you might prefer the Marshall or Mesa models in the zoom. If you run it into the amp on the clean channel set the mid on 10 and the bass and treble on 0. It sounds weird but that’s the amp’s “neutral” sound that’ll let the pedal take over without additional eq color from the amp.
That Peavey amp and zoom pedal should get you where you need to go.
good suggestions above for pickups- Nazgûl would be a good bridge choice. For the neck between the 59 and Jazz, the 59 will be slightly darker or more bassy, the Jazz being a bit brighter. Either would be a fine choice depending on which sound and vibe you’re after.