Step 1: Installation
The following commands both add repositories for the latest stack software, update and upgrade yourself, and then install the required system.
sudo apt-add-repository ppa:nginx/stable &&
sudo apt-add-repository ppa:ondrej/nginx &&
sudo apt-add-repository ppa:ondrej/php5-5.6 &&
sudo apt-get update &&
They should run fine! These applications all work on Ubuntu. In general, software that works on Ubuntu also work on elementary.
I'm running Apache and PHP in a virtual server using Vagrant, and that setup works well for me. You should be able to run these applications directly on elementary, if you'd prefer.
This is not the site to be asking that question as it is not related to elementary OS itself.
To answer your question: The easiest way is to download Apache, PHP, MySQL || MariaDB and PHPMyAdmin directly from the repos. This can be easily achieved by typing sudo apt install php5 mariadb-server phpmyadmin in the terminal. This is the easiest and more ...