Linux

Since you're just starting out with Linux, I'd suggest you start with a local server. That way you can try different things, even possibly fatal commands, and still easily reset the server. If you setup a remote machine and break it, without remote administration you'll have to call the remote sites administration staff and ask them to reset the server, which usually costs extra.

Also, servers usually aren't connected with a modem, but a run-of-the-mill NIC, connected to the Hosting Service Providers network.

I suggest you do a bit more reading before doing something that could potentially leave your box a slave to a cracker that infests/infects the rest of the world with bots/spam.

Yes, Linux can be pwned in a short while if left to a weak configuration and exposed to the internet.

I'd suggest you get comfortable with it first, perhaps in a virtual environment like VMware or Virtualbox.

Here's what I'd suggest when you want to build it out:

A DHCP server that can handle BOOTP.
A TFTP server
An HTTP(S) server for the install files

Read up on a PXE install for a linux server. What you would do is find out the MAC address of the network card, and then boot the server over the network and install that way.

You could, if you wish, boot it from a DVD or CD and then point its installer to a network share running NFS or FTP or HTTP(S). I would not expose a server to the internet directly unless you know exactly what you are doing. You should have a NAT and firewall set up so that you can do port redirection if you need any services from that server on external networks and I would suggest you look into port knocking for that too.