Personally I haven't had any issues with item capacity, I didn't even use the bank until I was running around at level 50 on mayhem mode and had enough legendaries that I couldn't try them all in a reasonable time frame.

When levelling up I take the view that a bad piece of gear in borderlands is like a bad haircut in real life, you'll grow out of it soon. Almost everything will be tossed by the wayside within a few levels, so it's not worth saving anything below level 50 even if you plan on levelling multiple characters, they'll get plenty of gear to run through the game with on their own.