We painted over ours. We just cleaned it well and then painted with latex paint. It worked great.
We are in the process of figuring out what to do with ours as well. I want to make our front door dark Kona stain. Then I want to finish it off with a marine varnish so it can handle the elements better. This is my plan because I think it will work better than what we have been doing in the past( staining, painting etc. and poly)
You can also get a marine paint as well. I have a friend that used that paint which is very thick and it has held up for years now.
Marine varnish or marine paint may be something to look into!
I like to use BIN primer-you can find it at Home Depot. Then use a semi-gloss paint.