I'm making a turn based online multiplayer game (matches are 1v1) where information needs to be pushed to clients every 5-10 seconds. Now from my experience and reading the best way to do this is through a server program I build with Java for example and run on a dedicated server. The only problem is because I'm young (17) I don't have money to support a thing like that. My client will be Java and my server in PHP on a Linux-Apache webserver.
From here should I use long polling to communicate to clients or should I try to use sockets?
Will it be open source or private?
If it's open source, just release the server code and let people run their own servers.
If it's private, charge money for using the server, and if you get your sums right, the problem of not having money for the server should disappear.
In the short term, while there's not too much traffic, use a relatively cheap cloud service like Amazon. If you need real power, this won't last you long, but it will be sufficient to get you started. You won't be able to avoid at least some financial outlay upfront, but doing it that way should keep it as cheap as possible.
I would probably use sockets, but you should bear in mind that these are only available in modern browsers, so users of old versions of IE might be a bit stuck.