Hello,
What will be the simplest path to integrating FusionAuth with my app?
You can self host FusionAuth, in which case, yes, docker on AWS is a valid option. There isn't an AMI or FusionAuth offering in the AWS marketplace at this time. You can self host it using any of the options outlined in the installation docs. It's hard to know what to recommend as I don't know what system technologies you are deploying other parts of your application with.
You can also use FusionAuth Cloud for a managed offering, which means you won't have to manage FusionAuth at all. Learn more about that option here: https://fusionauth.io/pricing
Can someone "map out" what I need to do at a minimum to get such system up?
I'm not sure what you're asking here. If you want help setting up passwordless, I'd review the passwordless guide. If this doesn't help, can you explain a bit more what you're looking to do?