If you want to keep the look of natural wood I would use at least 3 coats of polyurethane. Then seal all the joints and corners with silicone caulk available at your local home center, get the kitchen and bath as it does not have the mildew inhibitors that the tub and tile one has.

If you want to paint it I would use latex paint most likely a semi gloss as it is easier to wipe clean. With this I would seal the joints first with a paintable latex caulk.

Hope this helps.
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BigT
There is a difference between ignorance and stupidity. The ignorant can be taught, stupidity is beyond our control.
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1.2 P. d. deppei Mexican Pines
2.2 P. l. lineaticollis Linis or Lined Pines
1.2 P. m. lodingi Black Pines
0.3 P. c. sayi Kingsville X Stillwater red bulls
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1.2 D. corais Yellowtail Cribos
1.2 M. s. cheynei Jungle Carpet
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1.1 L. g. californiae B/W Cali kings
0.0.3 M. f. flagellum Eastern Coachwhips
1.2 G. m. bottegoi Western Plated lizards