Been doing my own thing

[Estellios]

You will be able to HQ but it would probably require some if not all of the mats to be HQ themselves to get anywhere near 100% chance. Byregot's Blessing (50 Carpenter) and Hasty Hand + Steady Hand II (37 Culinarian for the latter) are incredibly important skills for anyone looking to HQ items so I would beeline for those immediately if at all possible. If you keep your gear up to date you can probably consistently HQ most at-level items once you've learned those skills.

Regarding dungeon gear, most people I have run with in DF just pass on dented/worn/worm-eaten stuff so Need it if you can. If the group skips any chests with materials in them just go back and get the chest after everyone leaves. If they wanted the item in the chest they will do the same or just go to it during the run.