Actually, the file system you want to use for removable media that you want to be compatible with everything is exFAT (at least compatible with all modern operating systems / devices). Earlier versions of FAT have file size and file system restrictions you really don't want to be bothered with.
If the CAT solution above works, have at it. Likely the simplest.
If you do need a sound file editing suite that can do so much of this with ease, I've used Audacity for years. (just about the quickest thing for taking a blurb out of a song you love to make your custom ringtones)
Audacity is the world's most popular audio editing and recording app. Edit, mix, and enhance your audio tracks with the power of Audacity. Download now!
www.audacityteam.org
In this circumstance, you would just open all of the files in their own windows (or open one by one) - create a new file in another window (your destination mp3) - go to each one, in the order you want to play them and select all, copy, then paste at the end of your "to be" mp3 file. On to the next file (close the source files after you paste them into the new file, so you don't get confused and add them twice).
Cheers!