i have yet to use a humidity dome and have had 22 of 24 clones root, grow and flower over the last year. next time you start from seed the best way i have found is to grab some paper towels, soak them with water, fold them in half together, put the seeds on them and fold them in half again covering the seeds. put the paper towels on a dinner plate, and put the plate in a plastic bag. then put the bag with the plate in a dark area for 24 hours undisturbed. check the seeds after 24 hours, if they have not yet broken and started a root, fold the towel back over put it back into the dark area and check every 6 hours. good healthy seeds will start to root within 36 hours. once they have shot a root out, put the seed into whatever you are growing in with the root pointing down. if its soil that you are growing in make sure the soil is nice and wet. after you put the seed into your grow medium it will take another 24-48 hours to pop through the surface and expose its first water leaves.
as far as your plastic wrap goes, it will work, just take a knife or a needle or something and put some ventilation holes in the plastic. once the plant has its first set of sun leaves ditch the plastic .