I made a DWC system from a water pump in a 5gallon bucket and an air pump outside the bucket. The water pump brings water up through a tube to replicate a drip ring and the air pump aerates the water in the reservoir. It's very quiet and seems to work well. I modified a design I got from my local hydroponics guy where I also got the net pot and peat pellet.
I soaked the peat pellet in tap water that I'd left out overnight to evaporate out the chlorine. I put the seed in the hole in the top and pushed some peat over the hole. I kept it on a plate under a bowl in a drawer for a few days like I would do for the paper towel method. Then I put it in a rock wool cube. It didn't quite fit and I was worried that I might have hurt the root while forcing it in but it looks OK. Then I put it under my light and waited for it to sprout. Now that I've got a sprout happening, I'll plug in the DWC system and put in some starting nutrients.
This is my first time running a hydroponics system after almost 10 years growing, so I'm excited :)