From what I've read, I would say it's the combination of the pickup and preamp. Supposedly, Leo Fender wasn't trying to create a preamp that would cover all the angles, but rather building something with a very distinctive sound that stood apart from his earlier creations.
To that effect, I bought the aforementioned Retrovibe Stinger preamp, which is purportedly a direct copy of the Seventies-era StingRay circuitry, and a Seymour Duncan alnico MM-style pickup for a Warmoth
"JazzRay Projekt" I'll eventually finish
(...once I work up the courage to stain and finish the damn thing!
).
As far as what to buy, my Standard Operating Procedure, which you've probably heard me mention before, is to find something that feels
"right" in my own, two hands first. After that, pickups, strings and electronics can usually be modified and cherry-picked to find the sound I'm looking for. For the latter part, I'll hit up YouTube for as many product demos as I can find. That's how I picked one, particular Bartolini product for
Fender Dimension projekt I've been working on recently.