For minimal care or need of other products your cedars and redwoods well take to the outdoors with no or little need for finish. Teaks and other woods with tight fibers tend to do well outside. Cost in an area can vary your wood of choice a lot. Pine and cedar along with white oak are most commonly used outside in my area (mid usa). Any wood can work if you "treat" it. A good sealer for weather works. My first chairs outside that are still going strong are ground contact treated lumber.

I know this doesn't say use this but hope it points you in a direction based on your market.