I'm finally getting serious about building my own solid wood exterior doors for my garage which have been damaged by rain/splash (particle board cores), using the techniques on the video @lew posted for me last year. However, that project was for a front entrance door and used mahogany. This is for a garage back door and yard tool storage closet, and mahogany would be overkill. But I do want a wood that can stand up, with proper treatment, to Houston weather conditions (heat/humidity/bugs/etc.) and that preferably won't cost me an arm and a leg. (Although, right now, any visit to the lumber yard seems to demand a few fingers....) What woods would the folks here suggest, and how best to preserve and protect them to hold up?

I suspect the arm and leg part isn't something you can overcome without waiting a year or so, but doug fir (if you can find it) might do well for what you want. My first choice would probably be white oak though.

1 hour ago, Fred W. Hargis Jr said:

I suspect the arm and leg part isn't something you can overcome without waiting a year or so, but doug fir (if you can find it) might do well for what you want. My first choice would probably be white oak though.

Around here, white oak is close to Douglas fir in price.  If you gotta spend an appendage or two, go for the good stuff.

How best to finish and waterproof white oak for an exposed exterior application? I'd prefer stain/varnish to paint.

There was a time when the first thing I would have suggested would be oil based paint, the deep color base with no tint. When it was available it looked very much like varnish once applied and did quite well in the weather. Alas, I can't fins any of it to use anymore. So, my suggestion now is to get a marine grade spar varnish. This is not anything you find at the box store. The better names are products like Epifanes and are found at (drum roll) marine stores. They are expensive and require many coats...so be prepared. I'll mention this based on limited experience. Last spring I refinished a redwood glider we have with McCloskey's Man 'O War spar varnish. After sitting outside last year all summer and it's back outside now in the direct sunlight for much of the day it's still holding up quite well. I'm sure I'll have to redo it over time, but for now it's doing well. I applied 4 coats.

38 minutes ago, Fred W. Hargis Jr said:

Last spring I refinished a redwood glider we have with McCloskey's Man 'O War spar varnish. After sitting outside last year all summer and it's back outside now in the direct sunlight for much of the day it's still holding up quite well. I'm sure I'll have to redo it over time, but for now it's doing well. I applied 4 coats.

Man 'O War is great stuff. 

https://www.woodmagazine.com/materials-guide/lumber/outdoor-lumber?did=628791-20210429&utm_campaign=wood-online_newsletter&utm_source=woodmagazine.com&utm_medium=email&utm_content=042921&cid=628791&mid=56378781540

What's wrong with using Formica by cutting it up in narrow strips and alternating light and dark colors?? I remember we put a formica top table out side for about 25 years and it out lasted the wood legs.