Zinnser CoverStain is a good fast drying oil based primer. The order is prime, caulk, paint. The reason for this is so that the caulk is applied over the primer because the caulk will stick better there than it will to raw wood which will equal longer lasting caulk life. Dynaflex 230 is the good stuff.

Also-
* If painting new sticks(trim), thoroughly scuff-sand all sides of trim once cuts are made...pre-primed or not!
* Pre-primed stuff is ALWAYS near worthless. Very cheap primers are used, & are months old by the time you see it.
* On trims that will surround an entry-door/exterior wall...prime the backside, AND end-cuts!
* IF you're fussy, apply 2 coats of the primer PG said, wait a few hours, then very lightly scuff-sand using ~220-grit sanding sponges.
* Your trim will look even better!

Faron

Personally, I would use a slow drying oil primer

Enamel Underbody Primer (217)

Cover stain is great, it just dries to fast