I just don't even know where to begin. Is this something I could stand up locally and push to like s3, spin up a new server and install 1 thing and have it pull the configs and software installs down?
Any suggestions?
Yes. You could use shell scripts, Ansible, Salt, Puppet, whatever. I'm fond of Ansible or shell scripts, depending on complexity.
Start here: http://www.opsschool.org/en/latest/config_management.html
My opinion is ansible. Basically python + yml, you list out steps to set up your server. Takes a few minutes longer round 1, but you can remake the server in 60 seconds in 6 months. Lots of ansible tutorials around, try it out..
user data lives in redundant databases / storage service
server setup lives in a repo via bash scripts or ansible etc (and bake that into an ami or container)
setup your launch-configuration for your servers to setup all of the above and you can destroy and spin up servers on a whim