As for your edit...spend cores on opening factory slots and expanding your tank storage. Once you've done this (storage expansion will be an ongoing thing), cores are best used for events. Either you buy supplemental event currency with them to make up for not being able to finish all the event tiles or you can purchase the extra event tanks directly with them (for this event, PT-76 and/or Katyusha). Once your 'basic game needs' are taken care of, they're basically just another event currency.

If you're FTP, I don't recommend spending them on any recruiting. That's whaling territory.