If you use biscuits, the glue will be binding the biscuit to the wood
inside the melamine, so you don't have to worry about the glue sticking
to the melamine.
If you want to use screws, you can get little white plastic screwcovers
- some stick directly into the philips head of the screw, some are
basically white stickers, or you could countersink the screws and get
white plastic plugs.
Try
http://www.leevalley.com/hardware/pa...3,41306,41316f
for white plastic screw covers.
Will it be strong enough? I think your design sounds stronger than
many of the pre-cut, assemble-at-home MDF bookshelf kits you get from
Target or whatever.
If you're really worried about sagging, my only suggestion would be to
put a vertical strip of white melamine (or whatever) under each shelf
to help support it, or on the front of each shelf like a face frame.
Remember to use good dust collection and wear a mask when cutting MDF -
not very good for you.
Good luck,
Andy