I'd say unless all your boxes are full (and that's after buying the organizer that gives you 6 pages), you have no need to throw anything away. Even garabge from combining can be sold.
Then try to start combining all your junk like bugs and berries, see what you find really useful. The things you don't need/want, sell.
Then if your armor and weapons are advanced enough to where you don't need things like rare-1 monster parts, sell those too. I say that with a little apprehension because I've always found that I'll be inspired to run down a new weapon tree, but I sold parts that I needed.
Basically: combine, sell junk, and if you still NEED more room, sell not-so-rare items.
Also, just remember to bring all the necessary tools to beat whatever quest (even if it seems a bit superfluous) so things don't just pile up. Exploit their uses as much as you need, it's what they're there for. Being prepared helps compensate for poor equipment/skill/online partners.