How can I attach small wooden shelves to the inside of a wooden shadow-box style of frame?

I bought a shadow-box type of frame, wooden, about 12 inches by 12 inches. I bought it from a craft store, unfinished (regularly $32, half price for $16). It has a glass door with a clasp, and I think it would make a perfect knick-knack shelf. It’s about 1½ inch deep. I want to stain it, and then make wood shelves for the inside, and hang it on the wall.

What would be the best way to fasten the wooden shelves to the inside of the shadow box? I am concerned that nails might split the wood, but I would consider it. Glue?