Okay- most older CD players can't read .wav or .mp3, some new ones can read .mp3 no problem others can't, they will usually have a list if file formats they can read printed on them. Some very old CD players can't read CD-R or CD-RW at all whatever file format is on them so you have a lot of variables to start with. CD-R is much better to use generally for your burning projects.What's your make and model of CD player, it might help to know?
If you just burn them as a data CD then it literally just copies the files and it won't be able to be played on a CD player. Make sure you burn them as an audio file. If you are using Nero this is pretty easy as it has an option for this, not sure about others because I usually only use that. What programme are you trying to burn them with?