They're are two different ways you can go about this:
If your goal is to simply turn this secondary machine into an appliance which you can stick in a corner and forget about, I suggest you look into
Smoothwall Express. Yes, I know this is (damn near) heresy for a bona fide slacker such as myself, but Smoothwall is designed to do exactly what you've described and it does it in a very secure way.
On the other hand: if you're looking for a new project to tinker with (and learn something new in the process) then Slack is an excellent choice, but keep in mind that you will need to put some time and effort into making it more secure. After all, this machine will be accessible from the big bad internet.
The general term for this is OS hardening, but some specific things you'll want to examine are:
- what services are running on the machine (ssh, http, ftp, inetd, etc) and how to turn them on/off etc.
- tweaking your ssh daemon to be as secure as possible (this may seem counter-intuitive, but port-scanners are easy to come by and at the very least you don't want to run ssh on the default port). there are many threads in this forum on this topic..I think I even wrote one at one point. search is your friend.
- recompliling your kernel to eliminate anything that is unecessary
- and as a caveat to something cww said..go ahead and do a full (or nearly full) install at first, but it would probably be wise to go back later and get rid of anything you didn't need and/or anything the machine doesn't need to run day to day.
As I said search is your friend and so is google. Hope this was helpful.