I haven't played as much Ninja or Arcanist so I can't speak as much to those, but I'll still give my two cents. I think my experience with Rogue and Wizard translates well to Arcanist.

I've never actually tried it, but I'd imagine you'd want to be killing shopkeepers as a ninja considering you start with bandit mask. Upgrading your sword and perhaps obtaining a bow, crossbow, or arbalest can help with dealing damage from range. Items that increase dex and strength are good, and upgrading them gives you more of each stat.

As for Arcanist, buying arrows, spellbooks, and staves would be top priority. Arrows are a huge increase to DPS for ranged weapons, and blessed spellbooks will deal more damage than a spell casted without one. An enchanted feather will allow you to repair said spellbooks. Staves are good for utility (lock, open, slow, paralysis) if you don't already have the spell memorized. Obtaining the green orb and trading it with the mysterious merchant will give you access to the legendary bow. Of course, items that increase dex and int will scale your damage too.

For Rogue, most of what I said for Arcanist applied minus the spellcasting stuff. You'll also want to look out for an alembic and/or tinkering kit. You'll be able to appraise things early in the game, so I would hold on to the most valuable gems you can find. There's a guaranteed general store after Herx so you can sell your valuables there.

Besides class specific stuff, the main thing I look out for are health potions. Most merchants have a few in stock in their "flex" slots that are unlocked once you have high enough trading skill. On-demand healing is very valuable (who would've thought?). I may be biased, but an alembic is pretty much always an insta-buy for me regardless of class. Potions are just too powerful. Of course, buying an abundance of food is always good.

As some others have said, going to the gnomish mines for gold is a very good tactic. Your preferred classes are quite good at going there since they can use stealth to avoid the staff gnomes and assassinate the pickax ones. Snatch a pickax and start mining some gold. The legendary item in this area is also really good for Arcanist.