The thing is, your amazon instance isnt static. If you restart it from the AWS dashboard, you will end up getting a new IP address and then will need to repoint your DNS entries.
There are a few extra steps in securing your site that you will want to do as well.
I used AWS as just a DEV platform to learn how to install, then I went with NetCup hosting which charges me about $22 a month for a 8 core xeon with 12GB memory for me to host whatever I need.
Im not sure how you go about using AWS to host a production server.
I just wanted to help you get comfortable installing it.