Check plans & carriers in your state on eHealth for a start.
With regard to your other questions, copay plans are OK, but at that age (5 - 17) kids usually don't go to the doc that often. I would consider putting them under the parents
HSA or using a limited visit copay plan if available.
As others have pointed out, a few plans have ER visit copays, but you can also cover that with a supp plan.
Check your state mandate on immunizations. Most states I am aware of do not mandate immunizations after age 5.