As far as I know …

Gear has a huge impact on Ventures, Quick or otherwise.

Ilevel is the stat for combat retainers.
Gathering and Perception are the stats for DoL retainers. Gathering is a minimum to gather the item, Perception for additional amount returned. It USED TO BE that Gathering controlled all that and Perception affected how much came back HQ, but that changed with Endwalker.

It is unknown whether Gathering, Perception, or both is used for Quick Ventures.