Welcome to the forums Mitchell
It's a good question as it's fairly open ended, there are a number of options open to you. How familiar are you with hosting websites and IT in general?
You should be able to get by using a shared server to begin with while you develop this game, which can cost in the region of $5/month. Shared servers are computers that are permanently connected to the internet that are shared by a number of users, hence the relative inexpense of using one.
You may want to look into having a shared server/web host that offers a server side scripting option such as PHP or ASP, as well as a database that you can perform quick calculations on. MySQL is a popular database choice.
Your options depend on what kind of experise you have at the minute in developing the game, how much time you have, and your short and longer term goals.
If you haven't already, I would think about using your home PC as a development webserver. If you are using Windows, WAMP is popular (Windows/apache/mysql/php), while LAMP is the linux alternative. This would allow you to develop your website/game without paying for a shared server, though the shared server option is handy if you need to show other people.
Feel free to expand a little on how you envision of how the game and your website in 2/3/4 years time. Do you know of any prerequisites you need that are specific to the game?
as a wee FYI, please check out the ToS [webmasterworld.com] and the forum charter [webmasterworld.com], 99.9% of topics can be covered without mentioning specific products or URLs.