What is the best strategy for using things effectively?

First off, remember that you can always get more another copy of a thing sticker after you have used the original (I actually always put my first copies in the museum), so feel free to use them at your discretion. As for boss tips, just check out the surrounding level/world. I was able to guess what things I needed for every boss fight before they started fairly easily (except the one mini-boss that required a thing that I didn't expect to fight). For example the flag blowing in the wind on top of the first boss level indicates you need something that blows, the name of second boss level indicates you need some sort of sporting equipment, and the entire nature of the third world hints that you might want something that can clean up poison.