I'm with Adjor:
I don't like to germ in a paper towel or anything like that. Go right into a medium, the way nature intended. If your using soil start them in soil. If you going hydro put them in rockwool or your favorite 'starter' style plug. I think the paper towel method actually slows things down, and the risks just aren't worth it. If you are starting with good genetics you shouldn't need to germinate them anyway, they should pop on their own fairly quickly. Even with bag seed it's never taken more than 6-7days to have a plant with it's first set of single blade leafs.
As for the dome, I only leave it on for the first 1-3 days, it hardly ever takes 3 days for them to break the surface and as soon as they do I take off the dome. Damping off isn't form the dome, it's from over watering.
This is MUCH easier with rockwool, and I don't advise using rockwool for seeds with the humidity dome. Just a couple of the 1" cubes with the dome on and sometimes I wouldn't have to water again for almost 5 days. I killed many seedlings form overwatering rockwool cubes. With the root riots, even with the dome I usually have to give them a light misting once a day.
Rockwool can also do some funky things with ph that aren't easy for a newbie to correct. My vote is always for root riots, rapid rooter, straight coco, or a nice soil mix if thats your twist, in a heated propagator for at least the first 48hrs. The heat and moisture are the two signals to start growing. Even with soil, a little heat will dramatically speed things up and increase your success rate. It's not needed but I believe it's worth every penny, especially if you like growing from seeds.
A tray, a dome, a heat mat, and your preffred medium/starter plugs will run you less then 50 bucks and will save you not only headaches but time as well. Some of the best $50.00 I ever spent, and now I only have to buy the plugs when I run out. Put seeds in plugs or medium, put in propagator, take dome off as soon as the break ground. It's almost fool proof.
I also use the heated propagator and root riots with clonex gel to root my clones, I usually have roots in 7-10days.