I was short of time in my answer last night and cut a lot of corners...Here is a better, I hope, answer to your question...
Audio files are broken into three basic groups, CD quality, compressed audio and High resolution audio. CD is the defacto standard as everyone knows what they sound like on their own stereo's. The CD has a word length of 16 Bits and a sampling frequency of 44.1.
Compressed audio is a remnant of the time when computers has very limited storage and making bit perfect CD quality files ate up that hard drive capacity fast. The result was a series of greatly compressed lossy file options, all of which sound worse than a CD and some sound like crap. Next came lossless compression schemes like FLAC, which result in files smaller than CD size but are much bigger than compressed schemes. Apple through their MP3 driven iPOD made compressed audio a standard for an entire generation who liked the convenience but had never heard audio reproduced well. Folk who wanted better sound tended to drift into vinyl, which was fussy but cool and very trendy.
Today computer storage is vast and external drives can make it unlimited for very little money.
The heart of the hardware needed for music is the DAC, digital to analogue converter. It takes the bits of a digital file and converts it into music. All CD's play at 16/44.1...Modern CD players, separate DAC's, and many, many portable devices use DAC's that are capable of playing files of much higher resolution. Most are either 24/96 or 24/192 with the bigger the numbers the bigger the file needed and the better sounding it CAN be...
I say CAN because no amount of file size will fix a crappy recording and a MP3 will always be an MP3.
ALL iPOD's are limited to CD quality sound by their DAC...Many phones have much more modern DAC's. My Droid III has a 24/96 DAC meaning it can play files capable of sounding much better than a CD or an iPOD BUT, only through headphones or hard wired to an external audio system. The Bluetooth wireless signal is limited to CD quality.
High resolution is all the rage in serious audio today. While I own a CD system, 99% of my music is sourced from one of my computers to an outboard high resolution DAC and then to my serious stereo. Even my basic laptop, the one I am typing on now, is full of high resolution music that goes from the PC to a USB DAC and then to powered speakers.
Now, you asked where to get music better than the lossly stuff you noted. I recommend HD Tracks..
https://www.hdtracks.com/index.php?file=staticpage&pagename=audiophile_96khz
If your audio gear is decent, the better sound might surprise you.