What type of resources do cards like Tarkin/R2/Command Center/etc and the locations provide? Just Neutral? or the same type of resource they cost themselves?

The rules for resource matching say that to play a card you must use a resource that matches the affiliation of the card you are trying to play.

Tarkin produces Imperial Navy resources.

Mon Mothma produces Rebel Alliance resources.

R2, Dagobah training grounds and Sith Library would be neutral resources.

It all boils down to if the card has an affiliation logo on it or not.