In general, I will fire the bottom or "under" barrel first.
Theory is, that barrel is more in line with the axis of the gun ...so you get less muzzle jump.../ maybe its true, maybe its not ...but to me, its more habit than anything.
Habits or routine are important ...if you are on a station where you can only load one shell...( like station 8, High House, in Skeet )...I want to just load the gun, not overthink it or get out of my routine - or lose my focus on what I should be thinking ( which is about seeing the leading edge of the target ).....
Even if I switch the barrel selector to fire the top barrel first on a sporting station / I always switch it back to the bottom barrel first before I clear the station ( just part of my routine - as I clear and open the gun before I step out of the station).