You'll need a static IP address from your service provider, which you can then use as your web server's address. Check with the registrar of your domain name for specifics on how to update this information, they are all a little different. Unless you are getting massive amounts of traffic, you will probably find that your DSL connection servers up plenty of bandwidth. For a single server, a T1 line is not necessary...it would be kind of like taking a drink from a fire hose instead of a garden hose when you were thirsty. You'd waste all that excess bandwidth/water.
From there, it's a matter of installing some security -- a hardware firewall would be a good idea -- and setting up your server with the software you need. Remember that once you begin propagating your IP address change through the DNS servers on the net the current website will cease to exist to the public; make sure you have your server running properly!!