Option 2:

This option is a bit more complicated, but at the end of the day if quality of sound is important to you, then this might be a better option by far.

For this technique you'll need to download an additional program, called Audacity, and also download and install a plug-in for Audacity. Don't worry; it's much easier than it sounds.

This technique basically entails playing the song you want in iTunes, while recording it at the same time in Audacity. Audacity "listens" to what sounds your computer is making and records that, so make sure you don't have any other sounds interfering with the music while you do it!

Let's start:

1. Download Audacity and install it.
2. Download this zip-file and unzip the contents of this file in the same folder where you installed Audacity. (If you're not sure how to unzip a file, read this article.)
3. Open both Audacity and iTunes.
4. In Audacity, go to "Edit" and click on "Preferences".
5. On the "Audio/IO" tab, make sure the Recording Channels is set to "Stereo" (the default is "Mono").
6. On the "File Formats" tab, go to "MP3 Export Setup" and choose a Bit Rate from the drop-down menu. 192 is a high quality setting. Click "OK". (If nothing is listed under the File Formats tab, then ignore that for now. Step 15 will make it clear why nothing is showing now. After you've exported your first MP3, come back to these settings and then change it.)
7. Still in Audacity, find the drop-down in about the middle of the toolbar, that will have one of the following settings selected: "Wave", "Line In", "CD Player", "Microphone", "Stereo Mix" or "SPDIF In". Make sure that "Stereo Mix" is the one selected.
8. Now find the song you want to play in iTunes and select it so long. Don't start playing it yet!
9. Go back to Audacity and click on the big recording button at the top. Audacity will now begin to record any sounds that your computer makes.
10. Quickly go back to iTunes and press play. Wait for the song to finish playing and then press stop before it begins playing the next song.
11. Quickly switch back to Audacity and press stop.
12. If you want to get rid of the silent parts before and after your song that you recorded, read this article.
13. Still in Audacity, click on "File" and then click on the option that says "Export selection as MP3" or "Export as MP3", depending on whether you selected a piece of the MP3 or just want to export the whole recording.
14. A screen now appears that asks you where you want to save the file. Select a place, give the file a name (I suggest a different name than the original to avoid confusion) and click on "Save".
15. This is where Lame now comes in... When trying to export an MP3 for the first time in Audacity, a screen will pop up saying you need Lame to encode an MP3 and specifically a file named "lame_enc.dll". It also asks you to "independently" download this file and then asks you whether you want to locate the file "lame_enc.dll".
16. Since you've already downloaded Lame and extracted the files (including the one Audacity is looking for), click on "Yes".
17. Now browse to C:/Program Files/Audacity/lame-3.96.1 (assuming this is where you installed Audacity) and highlight the file "lame_enc.dll". Then click on "Open".
18. Audacity will now save the file as an MP3 to your hard drive. The next time you run Audacity and want to export an MP3 or a selection of a song, you won't be asked to go through the whole "lame" experience again.
19. Close Audacity.

Voila! You now have an MP3 version of your iTunes files with a higher sound quality than you'd get with option 1.