I'm re-painting the exterior of our home. Last paint application appears to be paint on the gable ends and dark brown stain on the lap siding. After all the necessary prep work and cleaning do I need to primer over the old stain if I want to apply a latex paint?

Yes, you should apply a good compatible primer that worksd with whatever paint you buy. Tell me exactly what you did when you preped and cleaned this old stained lap?

As yet I have not done any prep work on the lap siding, but it is my intention after all the necessary carpentry, fixture removal, caulking, siding nails reset, etc. to power wash the exterior; allow it to dry for a couple of days, then prime where needed and paint.

Do you know the species of wood?

Not really, but probably cedar. The home was built in 1977. Does not appear to have been painted after the initial paint application. The color is a dark brown stain that was popular in the 70's.

Might want to do a small test. Cedar will really get rough from power washing, raised grain, and then not have a smooth paint finish.