Paul - Couple of comments based on mistakes I've made in the past (nothing teaches like mistakes!). First (and most importantly) do not put a finish on your project until the other cabinetry actually arrives. It is -not- possible to match wood finishes from a photograph.
Second, use an alcohol-based dye to achieve your color. Yes, they are not as light-fast as water-based dyes, but if you're a beginner with this, it will be far easier to match a color with an alcohol-based dye because the water-based powders color shift quite a bit from wet wood to dry.
Third, don't attempt to dye the wood. It is far, far easier to use a toner over an initial clear finish coat than to actually dye the wood. A toner is simply a finish coat with dye added. I would recommend shellac because it's 100% compatible with alcohol-based aniline dyes. If you don't quite get the color you want, and as long as the color you have is a bit lighter than the color you wish to achieve, adjusting it is simply a matter of adding another thin coat of colored finish. This also works to adjust the tone of the color - if you want more red, then add a few drops of red to the colored finish and give it another coat.
After you've got the color where you want it, simply coat the piece with the top finish of the customer's choice - shellac is compatible with everything.
Finally, realize that you will either have to un-mount and take a cabinet door with you to match in your shop, or you will have to match on-site. Colors look quite different under different lighting, and what may be a perfect match under your shop lights is glaringly different in sunlight or the customer's lighting.