I plan to use Amazon Linux AMI to run a webserver. So for now, I only need apache, mysql and php.
Is there anything else I can remove to improve the security and performance of my installation?
The official amazon images come quite minimal with only a local sendmail daemon, ntpd, dhcp client, crond, atd, rsyslog and a few other services running. Based on this install and the default security groups, the Amazon Linux AMI is already as minimal as it can be.
Your question is not so clear. The general idea is to install and run only what you need. Running services that you don't need will consume more resources without any benefit. You can start by a clean system and install just what you need. That's it.