Ummm, while it's true that they do have a preferred type of weapon, you should just ignore it. It's just 20% extra stats from *that* weapon to the Hime who prefers it. So a 2000 Atk Gun gives 2400 Atk for Mammon and 2000 Atk for everyone else.
However, unless you're an ultra massive, space-time continuum bending whale, you don't really get to choose what is in your grid and what isn't. You'll just use your best weapon skills.
So, the order priority is really simple:
1. Same element, wrong type SSR.
2. Same element, wrong type SR.
3. Doesn't matter.
And everything that happens to be correct type just happens to be a small bonus. You pick your team based on Hime skills, NOT based on their Weapon preferral, after all.