One instance of every red-texted weapon in the game is stored in the bank with the exception of Atlas (because there are few enough that it’s not a burden on that guy’s backpack) and and Eridian (because he plays specifically with gear found in the wild).
The other characters keep no weapons in their backpack - when they roll a mission, they pick four on-brand weapons from the bank to take into the field, and that’s it. When I’m done playing, I return to Sanctuary III and put them back. (As I type this, I may change this behavior - when I load a character who has no weapons loaded, the trinkets are forgotten, and I have to re-select them every time. If I leave the last used weapon set equipped, it keeps the trinket assignments, and reminds me which weapons I used last to make it easier not to use them this next round.)
This leaves the characters’ backpacks available to carry a slew of COMs, shields, grenades, and relics to fit their various builds, with room to pick stuff up while playing. The bank also has some of these non-gun items that none of the characters have yet claimed, and I’m slowly whittling these away (or keeping just to have a copy of everything; my goal is to not have anything in there but guns and collectibles). All the COMs are cleaned out, the remaining few relics are good, I’m worrking the grenades down now, but I have quite a few shields that’ll take a minute to clean. I was hoarding this stuff for people that might ask for them, but nobody was asking, so here I am throwing out a bunch of Fish Slaps, Deathless relics… I just sold a freakin’ Vindicator Ghast Call. I need to get more comfortable with this.
I have a mule from a couple level increases ago, who was keeping all my good terror-anointed gear from the first Bloody Harvest (just to make it easier to find regular stuff in the bank), but I’m probably going to drop him… terror-based builds aren’t something I’m interested in, though I do keep like four solid terror items in the bank just in case.
As I type this, there are 50 spaces available in the bank.