Painting - oil based paint on the bath room walls

so ...new to this....
I just took off wall paper from the old bath...and found under it flat paint then got down to oil based paint....I want to paint Now.

I was told to patch the plaster where need be....
then sand LIGHTLY....
wash down with TSP
then apply a primer......
nothing else is needed.
is the the right steps....?
For the ceiling it has old mold spots....we plan to do the same drill on the ceiling.......
any advice????

I'd wash with TSP first, then follow the rest of the steps in order. Quality primer and paint from a paint store instead of a paint department in a big store will help.

so ...new to this....
I just took off wall paper from the old bath...and found under it flat paint then got down to oil based paint....

Was there flat paint on top of an oil based paint? And did the flat paint on top of the oil based paint - wash off with the glue removal??? And I assume there is no flat paint on the ceiling - just oil based paint?????

If that is the case: (the walls should already be clean from the glue removal procedure)

First, kill/remove the mold/mildew with a commercial mildew remover. Be careful not to drip onto any carpet etc... which could be ruined by bleach.

Clean the ceiling with TSP or any good cleaning solution. Allow it to dry.

If you are going to paint (with a latex paint I assume) over the old oil based paint, you should prime with an oil based bonding primer so that you can convert over to the latex paint without any problems. Ventilate the bathroom well during and after priming.

Once primed, use a bathroom paint or a moisture and mildew resistant paint (like Zinsser's PermaWhite).

I agree with the oil base primer! Latex paints/primers don't adhere well to oil base enamels.

If the bath room has a shower, it's imperative that you use an enamel paint and as noted above, a kitchen and bath paint would be best.