Paint the Trim First, Then the Ceilings and Walls
Pros usually follow a certain order when painting a room. They paint the trim first, then the ceiling, then the walls. That's because it's easier (and faster) to tape off the trim than to tape off the walls. And you certainly don't want to tape them both off!
When painting the trim, you don't have to be neat. Just concentrate on getting a smooth finish on the wood. Don't worry if the trim paint gets slopped onto the walls. You'll cover it later when painting the walls. Once the trim is completely painted and dry (at least 24 hours), tape it off (using an 'easy release' painter's tape), then paint the ceiling, then the walls.
To Avoid Lap Marks...
To avoid lap marks, roll the full height of the wall and keep a wet edge. Lap marks are those ugly stripes caused by uneven layers of paint buildup. They occur when you roll over paint that's already partly dry. (In warm, dry conditions, latex paint can begin to stiffen in less than a minute!) The key to avoiding lap marks is to maintain a 'wet edge,' so each stroke of your roller overlaps the previous stroke before the paint can begin to dry.
To maintain a wet edge, paint an entire wall all at once. Start at one end, running the roller up and down the full height of the wall, moving over slightly with each stroke. Move backward where necessary to even out thick spots or runs. Don't let the roller become nearly dry; reload it often so that it's always at least half loaded. Keep the open side of the roller frame facing the area that's already painted. That puts less pressure on the open side of the roller, so you're less likely to leave paint ridges.