You don't even need a Raspberry PI.
You can simplify it even further. List of things you need.
1. Smartphone or DAP.
2. Car Bluetooth FM Transmitter (~$20)
3. USB to 12 V car adapter(~$10)
4. Existing FM radio.
You can set this up in 5 minutes. Connect the smartphone/DAP using BT or AUX cable. Select a free FM channel and you are ready to go.
Also, in the photos, the FM antenna is fully extended which is unnecessary as these FM transmitters put out plenty of RF power.
P.S. On AliExpress, you can buy both for < $15 while on Amazon it is around $30.
P.P.S. Just the USB FM transmitter is only $5 on AE. For the cost of a cup of Coffee!
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Yea, I did this using a raps-pi as well. Rasp-pi is nice in the sense that it can run a web server to select/enqueue/blacklist/ and what not. I can also ssh to it to download songs and automatically add to the playlist...
Along with the ability to blacklist and add new songs, I hope that I will eventually end up with a huge collection of only the best songs (for my taste)