To paint a large section without leaving lap marks, roll the nearly dry roller in different directions along the dry edge, feathering out the paint as you go. After completing the entire length of the wall or ceiling, move to the next section and paint over the feathered edges. For the second coat, apply the paint in the opposite direction. This crisscrossing paint application sharply reduces (if not eliminates) lap marks.
I do not mean to come off with an edge, however, this is an article for people hiring low bid, uninsured, one man band painters out to "hustle" a buck. Hire reputable, established companies or hire someone you know or have a strong referral from. If you are arguing over watered down paint, ticky, tacky deposits, buying your own supplies, you have hired the wrong guy.
Some contractors work on time and material others on a firm contract. I would never hire the former and am leary of the latter. A contractor may low-ball a bid to get the job planning to make a killing on change orders. If you say good morning to them, they charge you extra for that. If the contract is not very, very specific and extensively fleshed out or if they display their change order schedule prominently on top, show them the door.