I can't comment on the adult bikes, but my recommendations for 16" bikes would be:
Used Specialized Hot Rock 16". For families that don't ride extensively, this is absolutely the best cost for value ratio. The bikes are relatively light (coming in several pounds lighter than a Trek Jet) and have relatively good geometry. My daughter started with a 16" Trek Mystic (the girls' equivalent of the Jet) and struggled to go more than a block with it. We switched to a Hot Rock 16" and within a week, she was riding 4 miles at a stretch.
My kids ride at least 50 miles every month, so for us it made sense to invest in a high-quality, more expensive bike. These would be my choices for a new bike.
(1) Islabike CNOC (At 13.2 lbs, this close to being the lightest 16" bike on the market; the only other bike that's lighter is the often out of stock and much more expensive Early Rider Belter 16). Downsides are cost and the fact that it has a coaster brake
(2) Cleary Bikes Hedgehog. This is the bike my son has and it's great. Relatively lightweight, no coaster brake. Downside would be cost; it also has a pretty aggressive (bent over/less upright) riding position, which can be good or bad, depending on your perspective.
(3) Woom Bikes 3. This is a relatively new bike, which looks great, but is very expensive for a bike your child will only use for a year or two.