Although I'm not very sure if I could understand what you said for my English, generally "stuff" means "mono" in Japanese but depends on the context.

"I put my stuff over there" --> watashi no mono wo sokorahen ni okimashita.

"I returned the stuff to the store" --> watashi wa sore wo omise ni kaeshimashia. 

"Stuff", in the usual, casual meaning, is probably best translated by こと　(koto), but mono also works well a lot of the time. Depends on what you're saying, and how (polite) you're saying it.

I'm guessing you got the answer you wanted by now, but from a native English speaker's point-of-view, what Eiriasu and Ryoko said is also what I was taught and the nuance of what I felt and heard growing up and when I was often there as an adult.  If you keep studying though, I'm pretty sure you will come into your own understanding of the multiple use words like mono (e.g. thing, person) and koto (e.g. thing, situation, insinuation for offering advice).  That really is a good question though, as simple as it is!