I'm guessing that I want to do a data disk (my files are all mp3 or mp4). I'm not an audiofile so I just want to give my tunes to someone else to enjoy.
A CD has a max of about 700mb no matter if you're burning an audio CD or a data CD. But an audio CD (think of it as what you'd buy at your local music shop) can hold a maximum of about 70 minutes, a data CD can hold many, many times that because the files are smaller. You can burn an audio CD from mp3 files, but it won't be CD quality (which you're not looking for anyway.) So I would say a data CD is the way to go for your situation.
Also, is there a choice as to audio CDs or data CDs so that MB can tell me the correct number of CDs I need?
An blank CD is a blank CD is a blank CD. 700mb is 700mb. But as I said, you'll get more data (mp3) files burned to a CD than audio files. Insert a blank CD and in the burn dialog select data and drag files to the window. MB will show you how many disks are needed. Switch to data and select MP3 and the number of disks required will change. As you add or remove files from the 'to be burnt' window the 'total file size' and 'disks required' will update.
How much storage space does this playlist take? If it's more than 2 GB, you might be better off putting it on a flash drive than messing with CDs. You'll be looking at 4+ data cds at that point.
You can also burn a DVD which has a capacity of 4.7gb. This assumes that the receiving person's device can play DVDs that contain data (MP3s) and not a movie. I don't have any disks or DVDs near me at the moment, but I recall that when burning to a DVD the 'disks required' assumes you're using CDs. At my request Steven added an option (when DVDs are used) to "burn to one disk."
It really sounds like you haven't looked at the burn dialog. As psychoadept suggested, do so. And look at the section on burning on the Wiki.