- Getting hosting from a minecraft "company"
- Paying for a VPS
- Paying for a Dedicated server
If you chose a VPS, you get far more freedom as to what goes on with the server. The upside is that you are not officially limited to a certain # of slots (however bandwidth restrictions may apply). Another upside is that if you want to host a forum/blog, you can. The downside however, is quite a turn off to some people, the setup. If you are a beginner, then you may want to stop here. Depending on if you use bukkit etc, the difficulty can increase. There are guides out there on how to do this, so I won't go in depth. However, what I will say is that you will need root access to start/stop the server (in most cases.) Prices vary greatly from company to company. Recommended for Intermediate-Advanced users.
A dedicated server is the most elite kind, where you can fully utilize the raw power of the server. The upside is there are almost no restrictions on how many players can play, it is very fast and you have full control of the server. However, it has one staggering downside; price. The costs for running a dedicated server (without a way of making money off of it) are staggering, often reaching above $100/month. The setup is often the same as for a VPS. Recommended for rich kids and Intermediate-Advanced users (with a MBA )
That about concludes our introduction to minecraft server hosting, and remember, fattwam is awesome