I'm sure others with more knowledge will also post, but here's our experience. Most of our rooms have cheapy thin paneling, all of it old and all of it dingy gross. We cleaned it with ... um, True Green? "something" Green... I didn't scrub, but I did use full strength. This stuff doesn't need to be rinsed off, which I'm pretty sure the TSP does. I used a floor mop to clean - much easier. Let it dry, went over ALL with a sander, then went over all with a vacuum, and then a tack cloth. 1 coat Zinnser 123 primer, and then painted. It looks soooo much better now!

Washing the walls is an important step to get dirt and grime off. My mother always used dish detergent, and many years later the paint is still there.

I'm no expert, but the owner of the BM store said if the paint is oil, you cannot put latex over it without a primer. If it is latex paint, you don't need a primer unless substantially changing the color.

Remember that just because a primer or paint is of high quality does not mean that it will stick better to a slick or dirty surface. The prep is still most important. I would sand it. The only time I clean is when the sanding doesn't remove the dirt/contaminants. Most homeowner types need to clean because they do not do a thorough enough job of sanding. You don't really need to use TSP though. Dirtex or something similar is probably fine.