Just use iTunes...
If you have a Mac, it's probably easiest to use iTunes to make an MP3 version of your audio files. It's really quite simple, and as a bonus you don't have to obtain a separate software package.
First, go into iTunes preferences. In the "General" tab, you will see a button down on the pane labeled "Import Settings...". Click that and a new dialog will pop up. Ensure that the "Import Using:" selection box has "MP3 Encoder" selected. Click okay to close the Import settings dialog and then click okay to close the preferences.
Next step, we need to see what kind of files you have (this will be important for later). So, right click on one of the column headers in your iTunes playlist or the top-level iTunes media library browser. You will see a context menu that displays all the column types that are enabled. You want to ensure that the "Kind" column is enabled with a checkmark next to it. The "Kind" column will tell you whether your file is MP3, AAC, Apple Lossless, etc.
Next, select the files you wish to convert to MP3. Right click on them and look at the menu that pops up. In the list there should be a "Create MP3 version" option. If you select that, it will (wait for it...) create an MP3 version of your files (haha).
This will take a while as the conversion is CPU intensive. Once it is done, you will have two copies of each song (one AAC, one MP3). You can click on the "Kind" column header to sort your music into AAC, MP3, etc for easy segregation.
ETA: The "Kind" column will list MP3 files as "MPEG audio file" (MP3 is short for MPEG Audio Layer III). Don't worry—these are standard mp3's.