How to try?
The best way to try the free Unices is to have a spare computer at home to use for installing them. If you have an old pentium or similar lying around, then you can install Redhat, debian, FreeBSD, Open BSD, etc.
What's a good one to start with? Well, if you've got a fast machine, try RedHat as it tends to come with KDE or Gnome, both of which require quite a lot of computing power. If you've got an older machine, try FreeBSD or OpenBSD which are leaner. It is possible to install Red Hat to be lean and mean, but you need to know what you're doing a little bit. A little bit of experience with one of the BSDs will get you into the unix way of doing things. Debian is a good choice, but can be a little complex. It has some great features though, such as the ability to seamlessly upgrade the distribution automatically with one single command: apt-get upgrade.
I haven't really tried Debian on one of my home systems yet, I keep meaning to, though. In fact, I may do it tonight on my big home box, assuming that Debian supports Kernel 2.4.
Update: next day. Well, I tried putting Debian on gizmo. What an unbelievably painful install! And why should I go through all that hassle for a 2.2 kernel? I went back to Redhat 7.1. Unfortunately, RH insists you use either KDE or Gnome, neither of which I want to use, but I can sort that out later.
I did put FreeBSD on there briefly, just to check it out. Now there's an easy install. Debian guys, go look at how FreeBSD does it.