How much chassis stiffening needed?

Torque boxes and subframe connectors at the minimum.

Do you "need" them? Maybe not. But you don't want to crack the paint at the quarter seams either.

Depending on the use of the car you may want more. Like if you're going to set it up for aggressive street handling you'll want to look into doing more up front, like triangulation the shock towers and firewall (J bars or US Cartool braces) and stiffening the lower radiator support isn't a bad idea either. You can do it in different ways but the US Cartool kits identify all the spots that need to be reinforced.