AWS EC2 Security Measures

I'm new to Servers environment and I don't know much about Servers, only few basics.

I'm getting into this just now and I found out Amazon has a 1-year trial so I wanted to try it out.

I see that their Dashboard has a lot of stuff and looks like they are already thinking with security measures. So this is what I did:

• Created an instance of Ubuntu Server 14.04
• Created a security group where I set the HTTP and HTTPS open to everyone (0.0.0.0/0) and an SSH opened only at my IP
• Set an Alarm where in case of server down it restarts it
• Accessed via SSH and installed Apache2, PHP, PhpMyAdmin, and other stuff thru command line.
• I already had a domain so I connected the AWS EC2 to a subdomain of my own by changing a DNS and everything works fine.

Now, this is not production-mode yet, is still testing, but let's say I want to get it online for real. Are there other security measures I should take in order to make the virtual machine/server safe?

Or does Amazon do all the trick already with that Security Group thing?

Perhaps mine may sound like a stupid question, but this is because I'm a newbie to this world. In that case, be kind.