Playset Staining/sealing question

Not a deck, but similar.

I purchased a playstar play set.  It comes with the lumber required.  From communication with playstar, they use pressure treated yellow pine, kiln dry it, and apply some sort of stain.  Supposedly the stain includes a UV resistant agent of some type - however there is no mention of a sealer.  The lumber that was part of the playset appears pretty dry (kiln dried and probably sat on a shelf for a year or better).  There does appear to be some mold/mildew (its possible this is just surface imbedded dirt/grit), discoloration from the stickers, etc on this lumber.

In addition to the lumber from playstar, I had to purchase some ground contact yellow pine 4x4s, 2x4s, and 2x6s.  These are still pretty damp/green. 

The reviews I've read on these playsets all seem to agree that it is best to apply an oil based stain/sealer prior to assembly.

I purchased Ready Seal, Natural Cedar (Stain/Sealer, UV protection).  

My question is - how to I best prep the two types of lumber I'm working with to apply Ready Seal?

Some type of cleaner made of bleach and water, TSP, or something else? 

Is there a way to prep the green contact lumber for Ready Seal? Otherwise, I suppose I'll assemble the playset after staining/sealing the factory lumber and later this year come back and stain/seal the green contact lumber.

Do I need to apply some sort of prep agent/treatment after cleaning to ensure that the oil based Ready Seal absorbs evenly?

Thank you