Anything that can serve static web pages will work, you can even share it from Dropbox and people will be able to play the game in their browsers.

If you want free, a Github page is a good option.

As far as I remember, the only requirement is that you host it on a server of some kind. I haven't tested it, but I don't see any reason you shouldn't be able to throw it up on a Github page: https://pages.github.com/

That would depend on whether you need any server-side application for your game. Obviously, if you want to build some kind of multiplayer game, that's a yes, and your options depend on the technology you want to use for the backend. Otherwise, if the game sits entirely in the client, you can get away with just serving static assets from something like Amazon S3, which costs very little at all, or perhaps even Github pages.