I remember reading about drives/players that wouldn't read CD-R, but I've never encountered one in the wild.
Anecdotally, every time I've tried: A burned CD that works well with one reader works with all others.
It was a hobby of mine at that time. I tried a lot of combinations: I was working at a local hifi shop where we had all kinds of stuff rolling through to play around with.
They hold up much better if stored in a dark place. A spindle on a shelf that sees sunlight is the worst case and they can become unreadable in years.