You can trade trophies for items as well as regain health and sanity at the entrance of the museum so it is worthwhile using your characters turn to visit it.
Reserve Glyph
It is vital that you learn the 'Focussing' skill as this allows you to hold a useful Glyph in reserve when you get your next batch of Glyphs.
Tutorials
Although it is tempting, try not to skip the tutorials as they are useful to consult when you return to the game after a long period of time.