I'm not sure if you were clear enough. Did you prime everything or only the knots? For the trim and woodwork, is this unfinished trim? Or has it been stained and finished already?
Make sure you prime all bare wood. And if you haven't primed everything yet, rough sand (60-80 grit) the beam as it's probably dimensional lumber. Fine sand the woodwork and trim (180-220 grit). If the woodwork and trim has been finished with stain and finish coat, make sure you sand the finish coat off or your paint won't adhere properly.
I usually use 1 coat of primer. personally I use zinsser latex based primer. (I feel it covers better than kilz, but kilz does a fine job as well)
You will paint with your finish paint after the primer dries. If you want to avoid brush strokes, you can use a small foam roller especially on flat areas.
I've never had problems brush painting a finish coat for trim work, but have used the foam roller for furniture or cabinets.
If you are painting pine lumber on the beam, you won't have a very smooth finish. If you go with a glossy finish, you will show imperfections more than if you use flat paint. Most woodwork trim should be fairly clear wood and won't have the same problems.
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