For $300 you're better off buying used, probably some kind of hybrid type bike like a Trek FX, Giant Seek, Roam, or Escape, perhaps 5-8 years old. You can mount rear and front racks with match panniers for all your equipment. Two bikes set up this way can carry a lot of stuff...oh wait, you're taking the bikes camping and not camping on bikes....All right, ignore the racks and panniers then. But those bikes I mentioned are still good.

As for your son, a five year old is probably riding a 16" bike, so any old one will do until he grows out of it. You might also consider a tag-along type bike so you can take longer outings without tiring him out.