First things first. You don't need to hook you computer up to your modem directly. That defeat the purpose, unless you were only going to be accessing the server from servers outside of you home.
Next you said that you might want to get a wireless USB internet adapter. I wouldn't recommend that. The reason being that even the best usb adapters are only going at 54kbps. If you have a wireless router that is fine, but you need a router for this. I would recommend connecting the server to the router with an ethernet cable. That way you will know that the connection is always there, you don't have to worry about loosing signal. Then you can just connect the router to your modem and you should be all set. You will probably have to do a power cycle but that isn't anything big.
Also if you do decide to set up this server i would recommend getting Webmin. http://www.webmin.com/
This is a frontside GUI that will make things a hole lot easier for you with adding users and other admin tasks.