I'd go to houzz.com and look for bookcases as an inspiration...once you find one you like, you can have your carpenter do what he can to replicate the style.

Usually you want to paint the shelves to match the trim in the rest of the house and use a semi-gloss paint.

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I'd chose the same white as your trim (assuming your trim is white).

And the paint finish should probably be the same as your trim as well. You don't want it flat--it will pick up fingerprints and dirt like crazy. Semi-gloss is probably best. Don't put books on the shelves until the paint has cured, so give it plenty of time, at least a week or two. The pressure of the books on the paint will cause them to stick, even if the paint feels completely dry to the touch. (Ask me how I know this.)

As for the style of Shaker doors, it's your bookcase. Pick out doors you like! I agree with the suggestion of spending time on Houzz, and will also recommend Pinterest. Find bookcases you like and show them to your contractor.

I have searched on Houzz for weeks and weeks, put together a bunch of pics, gave them to my carpenter, we designed the book case, but I am having such a hard time with the door styles! They all look alike!

Do you have a drawing or something of what you are planning? Depending on the design, the actual door style may become part of the background so to speak.

Have you gone to a home depot or lowes? Perhaps seeing them up close and personal will help you decide. There really aren't very many door manufacturers and so the styles can be pretty consistent regardless of the line chosen. And shaker style is pretty basic...just a frame around the outside of the door with a flat center. It's a classic.

"I prefer Shaker style, but there are hundreds - maybe thousands - of shaker door styles."

"...but I am having such a hard time with the door styles! They all look alike!"

There is a little inconsistency going on there. Take a deep breath, clear your mind...

Here is your basic shaker door...you don't want mitered corners on it. The center panel should be flat. I've seen them with a more casual look with bead board in the middle. But stick with the plain. Just about every cabinet seller will have something similar. If you like this, then you're done.

Yes - I do have a drawing. And no - its not inconsistent to say there are hundreds of styles of Shaker doors. Some have top and bottom rails that are more narrow than the side rails. Some have the opposite. Some have rails that are the same size all around. Some have mitered corners. Some do not.

What do YOU like? It doesn't matter if there are 10 thousand different styles of Shaker doors - choose the one that you like best. There is no "right" or "wrong" one.

Keep the top and side rails the same width, no mitered corners, and go with a medium width on the rails, not too thin, and not to thick.