We use and love Amazon Web Services for all of our server needs. They offer a free server in the cloud for a year too, after which it is like 20USD/mo for a micro server. All of our servers are based on their Oregon cloud, but you can get cloud servers at any of their facilities around the world. You login to your server using SSH via puTTY and winSCP (for Linux servers; Do not use Windows servers!).
We are presently using three servers and one database. One server for our security gateway/proxy, one for our game client, and one for our website/forums. All of our servers together with the database cost around 100USD/mo.
From there, you can use PHP/Python/Java based on a variety of installable software like Apache Web Server, Apache Tomcat, etc. Then you create an application program interface (API) for your client to talk to your server. Then you use AJAX to communicate between C2 and your server. You probably want a database (MySQL, PostgresQL, Cassandra, etc.) too, which you can either rent from AWS or install on your micro server yourself.
I can go into a lot more detail in PM if you are interested.