One important thing to remember is that you must be absolutely sure the TSP is thoroughly rinsed or it will cause paint failure due to lack of adhesion. Alternate and safer cleaners are ammonia/water or Dirtex.
The trim, once it's cleaned can be sanded to dull and coated with two coats of quality acrylic latex (Dulux Professional) or Waterborne paint. I prefer the Waterborne over latex or oil. They adhere and finish like oil without the yellowing, cracking and messy clean-up. My favorite, preferred waterborne (used over oil) is Muralo Ultra Satin flow enamel.
The walls, once cleaned and throughly rinsed can be primed with Gripper or other bonding primers like Bulls Eye 1 2 3. Then topcoat with your favorite quality acrylic latex paint.
I'd save the CS for another project that needs stain sealing and bleed protection and go with the water base primers (always). Environmentally safe, easy to clean up and IMO outperform oils for this application.
happy painting!
Michael