I rebuilt my front calipers with a kit and pins from RockAuto. Everything was high quality and has been working great for several years.
I'm usually a stickler for factory parts, but in this case just drop by your local auto parts store and buy whatever they have or can get fast.
I rebuilt my front calipers with the Carlson kit and pins from RockAuto, back in 2017, all for $20. No problems to report. The Toyota overhaul kit (04479-60020) is $42.20 from McGeorge and includes seals to rebuild both calipers.
I wouldn't bother keeping your cores. What are the odds that...
They're probably full of rust, then.
Unless you've verified runout with a gauge, they're probably not. The vast majority of "warped" rotors just have friction material deposits on them...