Whatever isn't nailed down goes to the inventory. (Of course, you have up to four inventories, and it's up to you to figure out which stuff goes into whose inventory.)
STMs are used when you need to ask or tell a character about, or request another character's help with something that you can't just put into inventory. (Note that if both the other character and the item are on the same screen, you can drag the item directly onto the character to initiate dialogue.)
Generally, don't worry about it until your attempted or expected solution calls for more sophisticated communication; don't stuff the STM with just about anything. For example, if you need to break into a security system, it makes sense to store the system in the STM and ask around, but don't worry about all those potted plants and paintings.