Help me paint my outdoor wood

[beachlvr]

OK, Google just isn't helping me today. I keep getting random links that don't answer any of my questions.

I need to repaint the outside wood door frame and windowsills on my house.

Today I scraped the loose paint off and used TSP to clean the wood. There's still a lot of dirt on the actual door, though. Could it just be stained permanently?

What do I do now that it's scraped and cleaned? I have a primer I was going to put on and then I will paint. Any other hints or suggestions from all of you experienced home improvement gals?

[2kCougar]

If the grain is really dark, you may need a special primer to cover it up. This is all that my FIL talked about when I was painting the porch railings. Personally, I didn't care, I just wanted them to be white. We will probably replace them with vinyl in a few years.
Make sure you use thin coats and watch out for bugs.