Originally Posted by
minupii
Running the server should be the least of your problems. Did you really expect your server to run with your computer turned off?
The fact that you would even go live on a self-hosted server troubles me, unless you have one hell of a connection.
A Virtual Private Server(VPS) is a partition of a dedicated server (in most cases) and usually comes with worse speccs than a dedi.
The perks of hosting on a VPS / Dedi could be, but are not limted to:
Constant uptime (almost). Usually a better connection. Hopefully a larger bandwith limit.
VPS's and dedi's usually have all ports open as default.
Most ISP's do not allow the hosting of servers.
Search google for more information about VPS's in general and where to get em cheap.
As for your first question:
Get a webhost or host the webserver with (example) a program such as WAMP of your server machine. If you self host the website you should subscribe to a DNS service and have them redirect your domain to your server public IP.