I agree that the simplest solution would be to use melamine shelves.
You can iron on edge banding. (No special tools needed)

David

wrote:

I'm planning my first woodworking project - a set of shelves in our
walk-in bedroom closet. 5 shelves each about 4.5' x 14". I was planning
on using 3/4" birch plywood for the shelves since I want them pretty
smooth. Each shelf will be supported by solid pine cleats running along
the wall.

What is the best type of smooth opaque finish to use on this? It has to
be perfectly smooth so none of our sweaters will get pulls as they go
on and off the shelves. Also something cleanable would be nice. It also
has to be white. I don't think paint is going to setup smooth enough or
be cleanable. What are my other options?

Thanks!!
-Bob