the doom 32X port detects which controler is plugged in, either 3-button or 6-button.
using two buttons to cycle through weapons is much better than one button cycling through everything single weapon to finally get to the desired weapon you need next to the one you had been using. if only there were a quicker way. there is - press the other cycle button.
otherwise the second best way is to use one button to select cycle by holding the button as you use the directional pad up & down or left & right to cycle through weapons. but that can leave you momentarily vulnerable to attack since you cannot move while you are holding the cycle select button. SEGA's mode button quick select method is better to avoid that vulnerability, which i edited in addition to my previous comment along with the START button.
using only one button for cycling can use more time to get to the weapon you want and if you accidentally pass it then you have to cycle through every weapon again. not the best control option.
when i play any port of doom i map the controls to be the same as the 32X doom port because its the best way to play doom especially on a six button controller. (holding C to strafe imo is better than L & R shoulder buttons that do the action. holding C doesnt do the action, the directional-pad does, which like the L & R button method also doesnt prevent you from moving other directions while holding C to strafe)
the 3 button layout is good too:
START = same
A = run. hold A then press START button to cycle weapon. (which is the same as one button cycling but with another button being held)
B = shoot
C = hold to strafe, tap to open doors & toggle switches, hold + START to select map
i dont wanna type the map controls.
32X port control method is the best.
the additional mouse🖱️in port 2 you applied is pretty kool to have as an available option