This is an idea I've been tinkering with for a bit. A hybridization of a scavenger set up I've been using and an infinite Tec9/spray and pray package.
This build would likely work on any character after you find a tec9, but ideally start with support characters like Karlee or Hoffman. Karlee for the mutation sense and opening tec9 or Hoffman for the team ammo buff.
This is almost what I think would be a Karlee roleplaying deck though. Scavenging for copper, ammo, and support items while calling out mutations and spraying down the horde with penetrating bullets. This build is initially aimed for recruit but adding in down in front would likely increase viability on higher difficulties by eliminating friendly fire.
Opening round set up the core of the build picking copper scavenger and money grubbers and immediately impact quality of life for the team with copper buffs.
Next two rounds sets up personal defense package with infinite ammo on the tec9 with ammo stash and fixing reload speed using speed demon.
Back to the support role the next two rounds, making sure your team finds more ammo, which you can stockpile and drop for them since you're tec9 uses none anyway, and support/medical items.
Marked for Death is a team buff that takes advantage of Karlees mutation sense and softens bosses and tallboys for the group.
After that core, it's all about making the most of the Tec9. I'm not sure if shredder impacts team damage, but spritzing enemies with increased bullet damage certainly won't hurt. Mag coupler to increase reload speed, quick kill and hunker down to increase accuracy and make the loss of aim down sights hurt less. Silver Bullets, Large Caliber Rounds, and Mag Carrier for bullet damage and penetration for swarm control as the rounds progress since your bullets will rip through the crowds of ridden at high speeds.
Last slot is a filler I guess. Could be avenge the fallen or inspiring sacrifice for team buff, but I had the last round of Act 1 in mind and making the most of Karlees Use speed.
Hope you guys enjoy!