I don't know much about the gazillion of actual chip trackers that exist, because personally, I've been hooked to Renoise for over 10 years, I'm still constantly learning new things. I love this thing.
The demo version works forever, you can save and load, just not render to .wav. It has demo songs in the help/tutorial section, and it's about the most solid piece of software you'll find. It also comes with a bunch of samples, which you could use with other trackers, and it has a neat sample editor to make looped samples: loop a very tiny sample, press a "note" on the keyboard, hold shift and release the note, and it'll keep playing -- then you can use the draw tool to edit the sound, which is fun especially if you've never done it :D
And check out the forums, if you dig a bit you'll find example songs and samples, especially chip type samples. You know, well tuned sines, squares and all that. Not sure how much of that comes packaged with Renoise, but that (and the arpeggio command that most trackers have) is really most of what you need to get some jolly good fun going.
The tracker doesn't matter as much as just doing it, I think. That is, in the beginning they're all going to be bewildering, so try some, find one you are comfortable with, and then stick with it for a while. Know that it's normal to feel like a total doofus, at least for me, the gap between the music in my head and what I ended up creating was horrible, and that can get better only if you stick with it. Read the manuals though, trackers have a LOT of keyboard commands, some useful, some mandatory. If you ever find yourself curious about VST:
It can load FastTracker II and ProTracker modules, and there's just so much great stuff to just load and check out, maybe turn channels on and off to see how it's made. I for one started out my derpy adventure with ripping modules and playing them in a tracker, for years, then modifying and sampling sampling things I liked, mashing things together, and making them from scratch came later.
Though most of those formats don't unpack to .mod files, I just wanted to mention this site. Sadly DeliPlayer (which ia a Windows version of DeliTracker on the Amiga, which along with EaglePlayer was like VLC for music on the Amiga) is no longer easily available, but there's XMplay + plugins to allow playback of many of those exotic formats:
But there's of course more, and if you have any further questions just shoot. I'm no expert and not up to date, but I've been into this on the side for over 20 years, so if you ask like that, I don't know where to start :)