This idea is quite simple: Make a collection of your favorite tunes using whatever software you like. Then stick them on a cheap USB stick. Then squish the cheap USB stick into some play-doh, and mix in your own bits of style, kind of like us geezers did back in the day when decorating the mix-tapes of yore. Present to your intended recipient, and explain that to get the music, they'll have to do a wee bit of play-doh archaeology.
Some notes based on my experience making mixtape Xmas presents for the family:
- I like to encode music in FLAC, because it sounds better and cause I don't like the man all up in my music storage formats. But unless your mixtape recipient is also a nerd like that, you'll just have to accept that MP3 is what most people can read. At least make them 320kbps.
- You'll want to include meta data and a playlist so that once your recipient copies the files to their machine, their music software will remember that they're actually part of a mix with a title and a specific order. Most music players can export a playlist (like an .m3u file). If you want to be thorough, you can use something like MusicBrainz picard to re-tag the songs as part of your mixtape collection.