I was once told by two industrial painters that best way to paint any exterior wood is to first make sure it is dry, then use metal grade oxide primer, like Rustoleum red oxide primer, on the wood BEFORE using any final coat of paint, then apply your final coat. Do NOT use any primer that is for wood like Kilz etc.
I did that to 2 doghouse over 15 years ago and they still look fine.
Believed I used oil base paint as top coat but not sure.