Game Servers Rental takes alot, and i mean ALOT of time. As previous posts suggests.
Unless you are available 24/7 then you will need to hire staff. This of course costs money on top of your basic setup, Dedicated Servers, Control Panel / OS Licensing.
You also have to think about your initial costs. Chances are your going to need a relatively powerful and expensive server for hosting your game servers, which won't come cheap, and then how are your going to host your company website, on th same box? I don't recommend this, although i have known companies that have.
Uptime is also very important. I'm assuming your a gamer yourself, and therefore you will known the important of the servers being online. When client servers start getting full and "populated" they don't want them to go down, AT ALL. Should they happen to, you'll be dealing with mass amounts of complaints - Should you have the customers!
Competing with GameServers, Velocity Servers, won't be easy. Not many customers won't want to leave there existing providers, as it means downtime and change of IP addresses (Important to many clans and public communities with popular servers.) You also need to think about how you are going to compete.
The bottom line is the industry for game servers is very demanding, you need to be able to provide support, low latency and reliable servers. Also, don't be surprised if someone 12/13 year old steals there parents credit card and purchases an expensive server without permission. Chances are they'll try claim it back in a fortnight, and Paypal aren't too good at protecting there sellers.
Don't start up the business until you've done your research, and don't get me wrong, if you believe you can do it, do it!