If you're aiming for MIDI music, there's two good pieces of composing software that I know of.
Noteworthy Composer 1.75 - I started with this one, and I still use it today. It's great for quickly typing down notes and playing them back, and you can do almost anything there is to do with General MIDI - changing instruments, multi-point controllers, and so on. Noteworthy Composer 2 doesn't let you export songs as MIDI, so be sure to get 1.75. The only downside is that the evaluation version only lets you save a file up to 10 times, but you can easily get around this by creating a new file and copy-pasting all of the tracks from your old song into the new file.
Anvil Studio - It's completely free with no limitations, though you have the option of buying special plugins for it, such as soundfont support. It takes more time to get used to, but if you have some extra spare time to learn the ropes, it's definitely more powerful and flexible than Noteworthy.
I currently use modplug tracker. I find it pretty easy to use, although some more advanced aspects are pretty tricky to learn. The biggest problem is finding samples to use. In that respect a Midi app would be much easier to dive in a mess about with.
Try as I might I've never got my head around any programs that can do what Noteworthy does in mp3 form. If you do get ModTracker, be wary that it might take you ages to produce anything decent, simply because it's impossible to look at and take all the information in properly. If only someone could make a ModTracker Lite...
If it's just MIDIs you're looking for, Noteworthy is pretty flawless, there are ways to do everything a MIDI possibly can if you look hard enough, like echoes, volume fades, panning, pitch changing.
i definately think you should start with Midi. Mod tracking can be hard to start out with. With midi you don't need to worry about even getting instruments, you have all the instruments at your disposal to begin with.