I have a couple of Milwaukee radios that I like. You can plug them into the wall, but you can also run them off a battery if you want to take them somewhere.
One is a radio with an aux port and USB port to play mp3s or whatever. This one does not charge the battery if the battery is in and it's plugged in, and the USB port will not charge your phone if it's plugged in.
The other one is also a radio, has the USB port to play off the phone, and Bluetooth. This one will charge your phone when it's plugged into the USB. It will also work as a battery charger if the radio is plugged in to the wall.
You don't need a portable radio if it's dedicated to the shop, but it's nice if you want to bring it out to the yard while you are doing something. I bring mine to family gatherings when we are out doing a BBQ or something.
Being able to use a drill battery is worth paying extra for instead of having something that has it's own built in rechargeable battery. one less thing to keep track of.
If you plan on getting something and leaving it in the same space, I would go to the second hand store (Habitat ReStore or similar) and by some old HiFi stereo. Mount the speakers to the ceiling in the corners of the building, this way the volume is the same level wherever you are working and the audio is decent quality. You can add on whatever you want to the receiver.
