Swashplate.
There is no 'rule'. The policy varies from airline to airline, and even within an airline as supply and demand changes over the years.
Many guys/gals get commands on aircraft based on their previous all round experience and ability. Flying the aircraft is, almost, a secondary requirement for the commander. Someone who has experience on 757/767 would very happily settle into 737 quickly.
I would guess that if you asked 10 different companies they would have 10 different policies.