Use the best weapons and armor for the current mission. There is a small box at the lower right corner of the mission selection screen, with "Best Attack" and "Best Defense" and two icons. This indicates what kind of element you should have for that mission. The types of elements are as follows.

Kinetic (bullet icon)
Corrosive (green drop icon)
Explosive (orange icon)
Laser-based (red laser sight icon)
Electromagnetic (blue lightning bolt icon)

The larger of the two icons is the most recommend element for that mission. When you go to the Scrapyard, each weapon and armor you can purchase has an element associated with it. Equip yourself as required by the mission.