How do I play MP4 on my MP3 Player?

Well, you can't play MP4s on a player that only handles MP3s, so you'll have to get your tracks into MP3 format. First, to go the iTunes Importing preference and set it to MP3 rather than AAC (which is the default). Then all CDs you import will be MP3. If you don't have that many CDs that you've already imported, I'd suggest that you delete any that came in as AAC and reimport; you'll get better quality that way. But if you have a lot, you can select the AAC tracks and use the Convert command to create duplicates as MP3. If you right-click on any header and select the Kind column, you'll be able to easily see which ones are AAC and convert them, and then if you wish delete the AAC copies afterwards.

Note that this will not apply to any tracks you buy, or have bought, from the iTunes Store. Those are only available as copy-protected AAC and cannot be converted to another format other than burning to audio CD.

mp4 is the protected AAC format for store purchases ONLY. Are you sure you're not confusing mp4 with m4a, the regular AAC format? If this is the case, in iTunes, edit>preferences>advanced>importing tab, simply change your preferences from AAC (m4a) back to mp3,

mp4 is the protected AAC format for store purchases
ONLY.

mp4 is a generic MPEG4 extension, m4p is the extension specifically for protected MPEG4 files.

m4a - unprotected AAC (or Apple Lossless) audio only track
m4p - protected iTunes Store track (currently only available as AAC)
m4b - audio book
m4v - MPEG4 video
m4u - MPEG4 playlist
mp4 - an unprotected MPEG4 file typically a video file

Note: For MPEG4 videos, both 'normal' MPEG4 and H.264 (aka. AVC or Advanced Video Codec) use the same file extensions.