Specialized crew are not bought, they are earned.
You can go to any Bar on any trade station, ask if they've got work, complete that mission, get paid, and there is a 1/3 chance that the bartender will hook you up with an out of work crewmember from the bar. You will need to pay cash to hire them.
You can also go to any colony, settlement or arcology and see the boss for work. Complete 3 jobs and one of the residents will volunteer to join you for free.
You will get paid for the jobs you complete for either of them.

Data Cores used in Advanced Cores can only be looted from Zirax Quantum Computers in Tier 3 or higher POIs and Ships (60% chance) or from the Tesch Overlord (100% chance for at least 2).

Thank you!

It's a 1-in-3 chance of getting a specialist from the bar missions??? Wow, I have terrible luck! From how often I get specialists, I would have thought it was a 10% chance, at best. :)

Also, is there a list of what POIs are what tier somewhere? I'm currently doing a self-challenge to gather the materials to build a ship that requires data cores. I'm not even close to the point that I can take on high-tier POIs yet, but when I am, it'd be nice to know what to look for and target. Obviously, I know things like Sector Commands would qualify, but are their perhaps any slightly-easier, not-so-obvious ones that would?

If it's a zirax POI with 12 or more turrets, laser fences around the walls and underground levels, it's at least Tier 3.
That includes Drone Bases, Missile Bases, Military Bunkers, Fusion Powerplants and The Sector Command.

Excellent, thanks very much, Vermillion!