Also, what are thoughts on .midi music?
The overhead for getting proper cross-platform MIDI playback is rather big - you will need a soundfont, and a decent soundfont is often dozens of megabytes in size.
Unless you want your software to run on *really* low-spec hardware (by that I mean anything below Pentium 2-class hardware), you won't have to care a whole lot about the format you're going to use. The best playback library out there is
BASS, which is available for Windows, Mac and Linux. It has the more accurate MOD/S3M/XM/IT playback. The CPU usage for these formats is very low, something close to 0% even on not-so-modern hardware - it can increase quite a bit if you use IT lowpass filters, though.
I have heard that .it may not playback correctly, is this true?
If you want 100% correct playback, this is true for any of the module formats. IT support is rather mediocre in some libraries like FMOD, however the same is true for many little details of the XM format.