Cedar is very good, but expensive...and I would still seal it personally
As Chadbot said, do *NOT* use Pressure treated wood (the green stuff)
I do not like pine because it is MUCH more prone to rot/mold....BUT I use it myself b/c of its availability and price.
Pretty much regardless of what wood you use, you should seal it with a good waterproofer so I go cheap on the pine and then just make sure to seal it REALLY good.
Personally, I use EITHER:
a) 635 3:1 epoxy from US Composites
OR
b) 2 coats of "weatherproof" stain (the can says it withstands hail and blizzard) and then a coat of DRYLOK on top of that.
personally though, I use epoxy on any bigger/"serious" builds, especially ones that house 100% humidity (like dart frogs, etc / glass enclosures). For open-air terrariums and things that vent out I feel the stain/drylok combo is decent but I'm still not entirely confident in using it.
I should say that I aim for at least 5, ideally 10 year lifespan on my builds.
You didn't mention what "kind" of door you are building....if you are just using a wood frame covered in screen, then option (b) should be more than sufficient (you probably don't need 2 coats even). Most of my builds use full size wood walls with very high humidity so my wood:water contact is much higher than simply a wood frame