Painting - repainting woodwork

I'm repainting interior rooms. Some paint on woodwork, especially doors is peeling. Don't know type of paint underneath, but top layer comes off with Goof-off. I plan to strip doors that are badly peeling before repainting, but what about areas with small breaks in top layer of paint? If the bottom layer is oil-based, which we don't know, what kind of primer should I use before painting? I have just been using liquid sander, then painting with flat latex, followed by semi-gloss. I think I will try 2 coats of semi-gloss because there have been places where I missed with the second coat (hard to see with same color), then they look dull. Any other suggestions?

Not sure what you mean by small breaks in top layer. If it's peeling, you'll want to sand what will come off. If it's stuck leave it and sand lightly to feather the area out smoothly. Prime with an modified alkyd primer that allows you to paint over it with any type of paint (Benjamin Moore QD-30 or other). Have your dealer tint the primer toward the finish color. Then finish coat.

Do not use paint as a "first coat" or primer, primer is primer, paint is paint. Do not paint two coats of semi-gloss without dulling the first coat. Shouldn't be necessary anyway. The tinted primer will be different enough from the final coat that you'll be able to see what you're doing.

Good luck

Sonnie