Careful pressure washing followed by complete drying follwed by 50/50 boiled linseed oil and mineral spirits. After thirty days or so, you can stain them the color you like whether it's a solid color stain, semi transparent, or for no color, transparent. Cabots, Sikkens, Superdeck (duck back) all make quality exterior stains with some including linseed oils in them that would save you a step.

The above suggestion is for the cedar. For the painted picket, you can carefully pressure wash to rid the peeling paint, fill any imperfections with exterior spackle, primer follwed by two coats of color. I would use an exterior acrylic latex for the topcoats. After pressure washing all of the above, replace any missing fasteners and check the existing or re-tighten.