Looks pretty good you might consider some diagonal bracing across the back. When tall cases are built without dados they are prone to racking. You can stop this by cutting a simple rabbit in the back and placing your back panel in it. But it is all ready built so adding bracing from corner to corner and gluing and screwing to every shelf it will help strengthen it You may half to half lap the center braces but it is well worth the effort especially when its on casters. As far as doors are concerned if you have access to a table saw or a router table you could build frame and panel doors. They are light weight and strong. Mount them with flush mount euro style hinges. Looks pretty good.