Hard to know where to start...
There are so many points here it's hard top know where to start.
Most modern music sounds crap because it's over-compressed at the mastering stage, where too many people think that making their content appear louder than anyone else's would make it sell better, whereas in fact it becomes a tiring muddy mess that makes people NOT buy music. And the technique doesn't work because a) everyone else is doing it and b) virtually everything you listen through has its own method of levelling things out that thwarts maximising. For more details, look up "Loudness Wars".
Most music heard on personal stereo systems whatever the make sounds crap because of lossy compression. MP3 - an ageing technology at best - is worst at this; AAC is much better but still not perfect. Lossy compression claims to remove the things you can't hear to reduce file sizes but in fact it removes plenty you CAN hear too. The only way round this is to use better compression, ie lossless. Apple Lossless and FLAC compress files without losing ANY data at all. Storage is cheap as anything now so why worry about compressing the crap out of your music (and the life out of it too) when you can hear it all? There are also new technologies in the pipeline that will deliver maximum detail if you have a special player and normal quality if you don't.
The main problem with listening on a personal stereo isn't the personal stereo, it's the headphones. Tiny little earbuds manufactured for pence are going to be hard-pushed to sound good. To get any kind of decent sound you will need something better - not necessarily over-hyped over-hyped names but good solid headphones made by reputable audio manufacturers at whatever price you can afford.
The last thing you might like to look at is the replay system. Your computer is not the best environment for music because it's so busy being good at doing other things. If you want to listen on your computer, however, you have many more options than you do if you want a personal stereo. To begin with you can buy an external USB DAC like Meridian Audio's Explorer or one of its competitors - a couple of hundred quid but worth it if you care about your music (and if you don't, why are you bothering?). Coupled with decent headphones, a good USB DAC can transform your listening, and the better the source, the better it sounds.
Hope this helps.