I’m not an AWS user, so the “Virtual Private Cloud” caveat confuses me. If I just click an EC2 instance, will that be in a “Virtual Private Cloud” or not? Also, are these IPv6 addresses publically reachable or not?
If you're not an AWS user yet then any EC2 instance you create (if you ever decide to become an AWS user) will be in a Virtual Private Cloud, either one you create yourself or the default VPC associated with your account.
Only older accounts (from before december 2013) have the ability to create EC2 instances that aren't in a VPC.
They are public. When you create an AWS account, you will have a default VPC (this wasn't the case with the classic EC2), and when launching an instance, if you don't specify anything else, the instance you launch will be in the default VPC.