Almost any wood is fine as long as it is encapsulated (totally sealed) in paint or like. Most paints will work avoid any designed for decks and bathrooms specifically as they have chemicals to prevent mould and mildew which I would not trust with a snake. Also avoid spar varnishes as the never truely harden and always have a soft finish.
I like poly urethanes myself colors in plastic I am partial to allow any paint or varnish to fully cure follow the instructions and allow extra drying time. I usually will 'bake' the paint by placing it in a warm really well ventilate space for a few days to help cure. I'd allow any solvent paint type product to 'out gas' for at least 7 full days and 10 days is likely better (and over kill)
I personally have worked with plastic products with the custom enclosures I have done. Being more durable and easier to clean but more costly and harder to work. My one other suggestion would be a plastic (fully plastic) bottom as it is way easier to heat through. I'd go with solid PVC (not expanded) as it is a poor insulator so it heats well. Wood bottoms can be difficult to get enough heat inside the enclosure.
mine...
http://images17.fotki.com/v147/photo...31/0128-vi.jpgHosted on Fotki