If the old trim is oil, then using a good bridge primer (BM Fresh Start 023) would make sense for all the molding - preceded by good sanding. A 2.5 or 3" angled sash brush should work fine. More important is that you select a high quality brush from the likes of Purdy or Wooster - use their best. As for the paint, RS is excellent as is Satin Impervo. You will see the name Satin Impervo or Impervo used quite a bit around here and sometimes folks are referring to the oil version, sometimes the waterborne. The oil leaves the finest finish possible, but since it's an alkyd, it does smell, it will yellow and requires thinner for clean up. The waterborne version also produces a great finish but has a bit of a learning curve. If you are patient, the result is worth the effort

Thanks for the advice, it makes sense. My contractor was telling me that I didn't need to prime, but if I am going to all this trouble I might as well do a good job! I think I'll start on the upstairs first, so that my skills will improve as I work my way downstairs.