Grim Dawn is moderately generous, and it makes me angry thinking about how D2 leaves you hanging out to dry.
Cleaning out the shared stash from time to time should take care of most of it, but if for some reason you absolutely need multiple characters to use the same item, it will get annoying. All my shields go to the shield guy, all my two-handers go to my Warder, and so on. What I tend to do is make mules for whatever character classes I eventually want to level up. This will be a big sanity saver, but it can be hard to find enough gear for your first character if you don't settle for yellow (magic) at times. You probably want to filter down to green (rare) quality at the lowest.
By the time you can afford it, you will have a ton of blue items. Your shared stash can be upgraded, but it costs a lot. You have to advance in the campaign to earn bag tabs, but it's tempting to level up in The Crucible for Devotion points instead.