cedar fence stain recommendation for Maryland

Hi.... on my own with a 22 year old cedar privacy fence. The back patio area gets direct sun in the morning. The fence has been stained before with Cabot (last in 2007?) and Behr semi-transparent stain (there are leftover cans in the basement). I saw some green stuff in a few spots which I successfully treated with "wet and forget" last year and it did not return. I repaired the fence last fall and now hope to get it stained soon before it gets too hot. What kind of stain would you recommend? Power wash only? Will the stain need anything added to it (I saw that one person recommended an algaecide)?

Thank you.