Hi cormate and Welcome:
I don’t think there’s agreement on what an “ordinary” CD player is but if it was “recently” purchased, it should play MP3 format. While this format will result in a loss of quality, for many people, MP3 (depending on the bit used) is acceptable. Additionally, you’re not talking about surround sound/symphonic quality so MP3 might satisfy your needs for this project. More importantly, it will significantly reduce the number of discs needed.
Yes, you can use a DVD but you’ll likely need a DVD player (and one that can handle MP3 format). I don’t know where you are but it might be worth purchasing a DVD player for this purpose as they have dropped in price. Be sure to take your finished disc to a store that will let you test the dsic on a machine you’re interested in.
Quick & Rough Math - I have burned approximately 200 - 3 minute MP3 format songs on a CD. That’s 600 minutes or 10 hours so you would need approximately 6 CDs (or 1 DVD)
for CD or DVD - your format should be Data CD or Data DVD
If you’re using Nero, there is an excellent post written by Jedi Master Yoda that can simplify creating the tracks. For example, you might want a new track every 30 minutes.