Are you dead set on two pickups? I have a bunch of basses with buckers in them. I was really gravitating towards dual humbuckers for a while, but am now finding that running dual pickups seems to cancel out more frequencies than they add. My EBMM 4HH doesn't sound half as good with both buckers on than it does with just the single "sweet spot" pickup selected. I paid more for that pickup that I never use... I also have an Ibanez SRX400 with a single sweet spot bucker and an Audere 4 band that, to me, is the absolute holy grail in bass tone - so even and responsive throughout the frequency spectrum that it often sounds "fake", like a midi synth (strung with DR Sunbeams).
That 4 band Audere Pro Z preamp is really great. I've got a lot of active basses with different preamps in them, but that Audere is the only one that I've used in more than one of them. The high-mid freq is really nice to boost a little bit to cut through a mix. That high-mid is also nice to boost going into a drive pedal.
Back to pickups: if I were picking pickups I would either go active OR humbucker, but not active humbucker. Humbuckers are nice because they are dead quiet, but their large size "sees" more of the string, which makes them a little less focused sounding than their smaller single coil counterparts. Having active singles is nice cuz they are dead quiet as well, and also more defined and focused. You can also achieve this with split singles. As for brand, aftermarket pickups are all petty great these days, so take your pick. EMG and Duncan both make nice actives. For passive buckers, Delano is top notch. Also Nordstrand, Aguilar, DiMarzio, etc etc.
Tuning machines... I'm sure I'll get people that disagree with me, but even my cheap basses stay in tune. Bass guitars are way more stable than guitars as far as tuning, so I'd say try and save some money on tuners.
As far as a piezo bridge, this is where I've gotta tap out. I've never had one. Maybe one day...