Set up EC2 instance using OL7.2-x86_64-HVM-2015-12-10 Amazon Machine Image (AMI) with three additional volumes of 5, 8 and 10 gb (this will make your life easier). I use additional sizes to accommodate increase in volume workload.
When setting up on EC2 the base use to login with is EC2
Login via MobaXterm as ec2-user and change password
Update tnsnames.ora, listener.ora files by replacing localhost with actual host name
find -name tnsnames.ora
find -name listener.ora
Restart listener and database
sqlplus sys as sysdba
At this point you should be able to connect to your database remotely with SQL Developer or your favorite tool, remember if you are shutting down your EC2 instance to first stop the listener and the database.