The shield backpack has a crazy long 8 minute cool down. If you get sniped by a bot soon after calling it and someone takes it, you've gotta wait a long long time to call in another.
As certified looter, I pick up anything I can and drop them so they don't have to wait for cool downs. As I personally don't use packs or support weapons that much.
usually, it depends on the mission. For bugs my usual loadout is : strike, cluster, 120 or 380 or both, rocket pod, orbital laser or mech. (support weapon will depending on if anyone takes for the mission, ie grenade launcher for bug holes/blits, if we need more AT then I pick EAT.)
for bots it's: strike, 120 and 380, then orbital laser or support weapon depending on the mission type. (40 mins then I pick auto cannon most likely if no one pick, blitz/eradication I just pick ems mortar. )
For majority of missions even if you don't pick a support weapon, you can get it around the minor POIs and just use them. I pick support only if it helps speed up the mission, not to get extra kills.