4. What is the best way to find out the quality of cabinets? Is it Cabinet doors that are more important to consider or Cabinet boxes? 

Cabinet boxes will never be seen since they are the bones of the kitchen and one can very easily be fooled by just looking at the doors. But it's the cabinet boxes that determine the value of the Kitchen. If a manufacturer is making the best grade boxes, they are probably making the best doors as well. 'You cannot judge a book by it's cover'. As a guideline, Cabinet boxes can be furniture grade or value line (builder grade or particle board), thus refered to as ‘GOOD’.  Furniture board are a combination of plywood and particle board sandwiched or layered thus refered to as ‘BETTER’. Finally, All Plywood Construction boxes are considered ‘BEST’ in quality. They are plywood slices glued together to form 1/2" or 3/4" thich box sides, back, top and bottom. Shelves and drawer boxes are 1/2" or 3/4" thick. Always ask what is the quality of a 'STANDARD' line in a brand and what are the 'UPGRADES'. The adhesive that binds the plywood must be FDA approved. Thus, it matters where the cabinets have been manufactured. 

Cabinet Doors vary in price depending upon the wood, doorstyle, base coat and top coat applied to it, and any special techniques used.  

A door maybe Slab, Flat Panel, Raised Panel, Reverse Raised Panel or Mitered.  Different manufacturers price their woods depending upon the demand and availability of wood and the finish applied to it. A door may also be made of MDF with a thin laminated sheet of wood or  a sheet of engineered product.  Most common woods are White Oak, Quarter Sawn Oak, Hickory, Maple, Alder, Cherry, Walnut, Birch, Pine or other wood more specific to the area. 

     Esthetics drives the look of the kitchen. When all the cabinet sizes that your kitchen needs are found in one particular brand, that's the brand recommended by your designer.