Skim Coating: Steps? Weight of joint compound?
I've done a lot of skim coating, mostly on old plaster walls.

If you're thoroughly sanding the walls, using TSP is not necessary. Just vacuum and wipe the dust off after before you coat. If you're going directly over a painted surface then TSP or other cleaning is helpful.

I've used lightweight joint compound. I prefer the setting kind (that you mix from powder and sets after a fixed time) and find the 120min set to be easy enough to work with. Setting compound is incredibly sticky and provides a long-lasting finish.

Get yourself the right tools (esp. wide-blade knives) and give yourself some time/space to practice. It's an art.