Making an open front (no doors) sheet-music cabinet. This is to replace a similar (garage sale) one that has failed. The failed on was particle board sides with 1/16"± shelves dado-ed every 1/2". The shelves were able to slide. I would like to re-use the shelves since they are thin and I cannot find similar thin particle board. Home Depot had masonite slightly fatter than 1/8 inch.

Anyway, the cabinet failed because the dado cuts broke through. I am contemplating using plywood for the new cabinet.
Advise needed:
1)What's a good grade of plywood for strength after cutting dados?
2)Should I laminate 1/8" masonite onto the the 3/4" ply. and make cut the dados through the masonite for strength and wear?

Note, this is not furniture, simply storage. I have over 20,000 song titles collected over the years and want to organize prior to my demise. All suggestions appreciated.

Ivan Vegvary