What Emily said.
We have a Mac and loaded all our CDs into iTunes on our main music library. Then, DH & I put the ones we each like into our respective laptops (also Macs). You are allowed a certain number of "copies" (whatever they call it). I am currently playing music on my laptop right now from really old cassette tapes I used to have!

We also have a nice stereo (from the 80s or 90s) and a couple iPods (older ones) and our iPhones (also older ones). We can and do play music on all these!
I would NOT get rid of our stereo. We have it hooked up to our TV and play movies through it to get better sound. We have my old iPod mini hooked up to the stereo, too, and play music through it. Sometimes we actually listen to the radio on the stereo. I know, old-fashioned!


We have a bookcase with doors on the lower half. I adjusted the shelves in order to get all our CDs compactly arranged. We did give some away, but these were the ones we would never bother replacing if we lost the music on the computer for whatever reason. We don't really buy real CDs anymore. We purchase the rights from iTunes or Amazon (and other places online), so we are not adding to our physical collection. If a hard drive crashes and we cannot retrieve the back-up for whatever reason (technology is great, but not infallible), we still have our favorite music in the original format and can reload it.
If space is a concern, you can weed out the least favorite. Then, you can toss/recycle the cases and put the CDs (and possibly the inserts -- personal preference) into a CD binder and toss that up in a closet. I recommend keeping it in the main part of the house (same humidity and temperature) in order to not cause mold or mildew issues with the binder and paper. Extreme weather can ruin CDs, too.