I've been trying to think of some music that's mixed especially well, but for me my attention is usually only drawn to the mix in particular when it has some deficiency. It could be too much or too little bass, an uncomfortable imbalance between the left and right channels, muddy or thin sound, etc. If something is recorded badly in the first place, that overshadows how well it may have been mixed afterward. If something sounds great it's usually because it was recorded well and mixed in a way that has no obvious problems, and, like I said, there is a lot of freedom in how that can be done.
I'm afraid I don't have music of my own to show as I'm not really a composer, just a hobbyist of the engineering side of music and a critical listener. Pink Floyd is the band that got me really caring about sound quality and I think their best-sounding albums are
Dark Side of the Moon,
Wish You Were Here,
Delicate Sound of Thunder (which is actually a live album, so that is quite a surprise), and
The Division Bell. All extremely well done on the production side and I love the music too. Queen is an outstanding example of the mastery of mixing considering the large number of instrument tracks and voices in much of their music, made even the more impressive considering the equipment they had at the time to do all that. But few artists are so ambitious as to even give an opportunity to tackle such a mix!
Your headphones sound like a good thing to use. If you intend to make music with synth, spending money on high quality instrument samples first would surely have a larger impact on your sound quality. Some will say you should mix with speakers to get a proper appreciation of the sound stage, but in anything less than an anechoic chamber that brings its own set of inaccuracies like sound reflections off the walls. You should listen to your mixes on multiple systems to get a more complete idea of how it sounds, but a difficulty with that is that you might expect it to sound like other music you have which is frequently made much too loud either in mastering or at the mixing stage itself (see
"Loudness war"). A good mix should not be spending all its time in the top portion of the volume meter. Also, remember to take periodic breaks to let your ears rest. You may have learned this from experience by now, but you can start to believe some funny things are improving the sound and then you come back and listen later and go, "what was I thinking?"
I repeat though, "Nekorush Theme" is mixed really well, my suggestions notwithstanding. In particular, the stereo panning of the main melody part and the background additions that build as it repeats. The volume of those background parts and of the harmony that starts at 10 seconds is very tastefully done; you can hear them clearly but they retain their subtlety. I'm sure it's easier to mix retro synth sounds than instruments with more complex frequency characteristics, but in most things you do you should strive to get a mix like that.
Of course it's best to get a recording that sounds good in the first place, but often you can enhance something significantly after the fact. Like with your issue of getting clear sound on your distorted guitar tracks, I bet EQ could go a long way to solving that. The problem is likely to be in the mid-bass region and a treble boost would also improve your sound. If you want, you could upload to a file hosting site some individual guitar tracks you want to layer and I could see what I can do with a mix and tell you how I did it if you like the result.