Next to its ammunition the catapult barely registers. Wood, a little high quality metal and two parts that come from loot: the gear is a Level 3 craft and the rope cannot be crafted at all, so both come out of crates and barrels. The gear is usually the one that keeps you waiting.
The research is the bigger decision. The catapult costs twice the scrap of a ballista and does nothing until a bomb blueprint follows it, so choose the bomb by your sulfur box. Propane bombs at 900 sulfur each are the ones for buildings, firebombs cost a third of that and are meant for wood, and bee bombs take no sulfur at all.
Tip
Craft the catapult last. It is one short craft at the Level 2 bench while the bombs take days of gun powder, so start the powder queue first and craft the catapult on the evening of the siege, once the horse is saddled.
Questions
Catapult ×10: how many resources?
High Quality Metal ×200, Wood ×5,000, Gears ×10, Rope ×10.