Nice work on the chair!
For outdoor finish here, I have found this stuff works pretty well:
https://www.amazon.com/MESSMERs-MC-5...s%2C171&sr=8-4
It is a bit on the pricey side, but does seem to do a pretty good job protecting from the sun. (At least here, the sun is far more damaging than water).
The only thing I did a bit different than the instructions call for is to thin it out about 2:1 (2 parts finish to 1 part mineral spirits). Then I applied it with a rag instead of a brush. Wait a full 2 days for it to dry. Then do at least one more coat (preferably 2 or even 3) at full strength, drying 24 hours between coats. The full strength coats, you can use a brush.