You don't "prime" wood for staining - only for painting. Although you may or may not need a sanding sealer, depending on the species of wood. So, to be clear, are you painting or staining?
You can't possibly match the smoothness of a factory finish. What you can do, is visit a good local paint/finish store (NOT Home Depot) and inquire. You'll need a stain to achieve the right color, a good, hard, self-leveling top coat, and all the equipment and advice to do the job as right as you can, under the circumstance.
Then, get a small container of their recommended products, and come home and test. Read, read, read about wood finishing. Sometimes you will need to waterpop the grain to get a finish at all like the original. Or use an aniline dye, rather than a traditional stain.
THEN make sample boards. Try different stains and then put multiple coats of your chosen topcoat over it and see how it looks. Not right? Try again.
If you're painting, alkyd paints have come along way. C2 Trim and Cabinet is a good one.
If you're staining, be aware that an oil-based top coat will usually impart a yellow tint when applied. If that is a problem for your color, go with water based.
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