I agree with watching Craigslist. Many sets sell for 1/4-1/2 of retail used. Stick with quality brand names. PDP, Tama, Yamaha, Pearl. There are many others but those are generally popular. If you're looking for new then you should be able to find a good deal on PDP or Tama. They both have quality beginner sets. Cymbals are definitely important, and the most expensive. You can get a deal by buying in packs. My son used cheap cymbals for a long time before we upgraded though!
Good luck and welcome to the family of parents who learn to ignore loud noises! Honestly, I barely even notice it anymore. We have so many instruments and my son practices so much that I've learned to sleep right through it.