3 Stages really;
-Big Crossbow W/Tripod (early game)
-Static Trebuchet (mid)
-Wheeled Catapult (late)

And I think the Plains is right for a wheeled catapult because
Open and smooth
Far into the game
Tough enemies which could chase down a crew

A big crossbow on a tripod would be fun against Trolls who come too close.

A Static Trebuchet would be fun against a Drauger village if they'd come out and attack the crew.