The decision also rests on what the quality of the wood is like that is used for the trim -- if it is "paint-grade" pine with those finger style joints of wood, then you might use a dark stain so you wouldn't see the imperfections. It's another story if the trim wood is more towards the furniture quality level, and something that would be pleasant to see with a light or natural stain finish.....

a bedroom doesn't have to match the trim in the living room. A lot of people think that every paint color, trim, flooring should be consistent throughout the house. I'm not one of those people. if you bedroom is visible to the living room, then I'd say yes. but if it's on another floor or hidden down a hallway, do what you like.

as for wood trim, what kind of wood trim? 80's oak?

Stained or painted white? either works. it just depends.

it's easier to vote if you show a picture of the room, the paint color on the walls, the flooring and any furniture.

Sherwin Williams Extra White in semi-gloss would make the gray really pop

I'm a big fan of painting trim the wall color and not calling attention to what is often pretty ordinary millwork. I do tend to go up a sheen for the trim. I like the simplicity it provides.

I'd look carefully at the quality of the millwork -- if the second picture is your house and I'd be reluctant to paint what looks like a fairly well detailed trim feature, with the nicely framed windows over the doors, etc. At least in that room! The bedroom might be a different story. To be conservative (or lazy!), you could just paint the walls now, leave the trim as is (assuming it's that light color) for the timebeing, and see how you like the combination.