Either will work. However, I was recently using some Zinsser 123 water based primer and it states not to use TSP. I don't know why, I'm new to that product.

I'm assuming your varnish is polyurethane. I would probably sand to get a smooth finish, then prime and topcoat. The sanding is light, just scuff sanding.

What paint are they using? I would recommend SW Proclassic Waterborne Alkyd or BM Advance. Don't let them use a latex "wall" paint, as it is soft and will be hard to clean.

I prefer liquid sander because of; less labor, better removes contaminates and gets in tight places. From the standpoint of health risk/comfort,if weather allow's open windows I go liquid. Wet or extreme temperature I go with sandpaper and face mask. A common mistake with many liquid sanders is waiting too long between wiping down and applying primer or paint. Read label.

Carlos, Zinsler123 recommends using TSP to clean up the brush; I believe shellac based Zinsler 123 somehow reacts to TSP. I would simply sand it down.

3M has scuff pads that can prep a surface without creating as much dust. The red pad is good before painting. Scotch-Brite 7447 PRO Hand Pad, 6 in x 9 in. is available at Autobody/Paint supply stores. 3M 7447 and Amazon.

I love Scotch-Brite pads. Keep red,green and white on hand at all times. Great point regarding dust dan.