Each side starts out with the equipment that they normally and have been shown to consistently carry on them.
For example, Daredevil would have his billy-club, but Reed Richards would not have the Ultimate Nullifier.
In a scenario fight, the contestants in whose city/reality the fight takes place are allowed access to any material resources they usually have there or of any team they're active members of, as long as they can reasonably get to them. For example, in a scenario set in the DCU, Green Lantern would have access to equipment in the JLA Watchtower, but not the Titans headquarters.
The fact that all chicks are bat-crazy, in some way. The partner must accept this and take it in stride, if they want the relationship to work.
Matt: I swear, Kim is nuts.
Jim: They all are. It's standard equipment.