Hi, Watrfall and Hunter (sounds like a law firm). LOL
Sealing drywall is pretty easy. But let's go back a step and do your new walls right. Zinsser's B-I-N is great for sealing dry wall for painting or papering. It will also seal a lot of marking products. Because they are all alcohol based, it may have a problem with fresh ink and magic marker. It might be best to try to "wash" these off with straight denatured alcohol. Just dampen a rag with the alcohol and lightly go over the ink. Don't rub. Let the alcohol relax and absorb the ink. Then apply a coat of B-I-N primer/sealer. I suggest applying a coat of B-I-N to all the walls before you paint. It will not give you a problem over the wall you have already painted if it has dried completely--a good 24 hours or more depending on the type of paint. Check the label. The Zinsser brochure that I have says that B-I-N is an excellent stain blocker for ball point pin ink and marking pens. If you use the B-I-N, you will want good ventilation. It will dry quickly. Check with your local paint store for their suggestions also. Other people like ther brands and Zinsser also makes water based 1-2-3. The Zinsser brochure says that 1-2-3 is only fair for blocking these stains. You will need the alcohol for cleaning your brush and roller frame too.
Alcohol is flammable so follow label directions and leave any rags or similar items outside for a day or 2 to dry completely. Don't leave the rags wadded up in a ball. You have to let the air get to them so they dry quickly and completely.