Deploying a Java web application to Amazon

I am sure this question has been asked and answered before multiple times. But unfortunately, I am still not clear. Here is my issue.

I have a JSP, Servlet application which uses MySQL as the database. I have built the WAR file as well. Now I am in need of deploying this so it can be accessed online by anyone.

I looked into lot of areas including normal web hosting. However even though the services like DailyReazor are highly secured, they provide little for MySQL, around 250 MB for the package I selected.

Now I am looking into Amazon AWS. In AWS I am expecting to deploy my aplication and make it available online.The MySQL server should not contain limits like 250MB.

But I have never ever used this service AWS before. By reading various posts, I know that Elastic Beanstalk is the easiest way to go, but still not convinced about how to deploy it properly with database access and all. And in the other hand, will they give me a web address like "www.example.com" or will they simply provide an IP address?? I am also familiar with tomcat so I need to use it.

We will not upload files (images etc) at the moment, so I believe we can manage with around 20$ per month?

I really appreciate if someone can provide a clear guidance on deploying java web applications in Amazon, with the requirements I mentioned about MySQL, Global access and so on.