ok, for the ones that are not protected with DRM (the ones purchased from iTunes) i.e, your ones that you've ripped from CD, it's easy peasy.
Open iTunes
Go to Preferences (I think Preferences is from the edit menu on the PC version)
Click on the 'Advanced' button from the window that appears
Click on the 'Importing' 'tab'
Change the 'Import Using' popup menu to 'MP3 encoder'
Change the 'setting' popup menu to 'Higher Quality'
Click on OK.
Now, find your tracks in iTunes that you wish to convert to mp3. I would create a new playlist and drag those tracks into it for ease of use.
Select the tracks and then from the advanced menu select 'Convert selection to mp3'
Bish bash bosh. Done.
The only thing you'll have to be aware of is that you now have two versions of each song you have converted in your library. Be sure to copy the mp3 versions and not the m4a (aac) versions to your sony player. You can ascertain which version is which by making the 'Kind' column visible. To do this, go to the view menu and select view options. Then put a tick in the 'Kind' box and click on ok. Now if you scroll to the right, you will see a new column, 'Kind' MP3 files are listed as 'MPEG audio file' and mp4/m4a/aacs are listed as 'AAC Audio file'. Note, the ones that are of type 'Protected AAC Audio File' are the ones you have purchased and there's no easy way to unprotect these and convert them to MP3. The best way is to burn them to an audio CD and then re-import them as mp3. Not the most elegant solution, but at least it will get you your iTunes music store purchased music on your sony player.
hope that helps
Stu