If the trim is hardwood, I'd leave it the hell alone, and decorate around
it. Painting hardwood is a sin, and the next owner may prefer the look of
real wood. (Another 10 years, and normal people won't be able to afford new
real wood trim.) But that is just me. On older houses, first thing people
usually want to do is take X coats of paint off of the interior trim, to get
back to the nice crisp original profiles.
If it is merely pine, a good scuff sanding (physical or chemical) and
degreasing/cleaning should give plenty of tooth for a quality interior trim
paint to stick. I'd do one room at a time- it is going to be a lot more work
than you think it is, sanding/scrubbing/painting in awkward positions,
whilst NOT screwing up the wall and floor surfaces next to it. There is a
reason people went with the harder clear finishes versus paint in the first
place- trim takes a beating, so the less often you need to mess with it, the
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