If you don't want to risk it on eBay for a vintage portable player, you can always go new with something like this Steepletone three-speed portable record player with radio.
Very much in that Dansette, Bush or Fidelity style, this lacks the valve amp of a vintage player, but does make up for it with some nice modern additions. Obviously, there's a three-speed semi-automatic deck, with audio through the front-facing stereo speakers. You also get the 'suitcase' container too, with handle for carrying round to a friend's house.
But you might not expect MP3 playback via USB/SD connectivity or the AM/MW/FM radio with manual tuning, which brings it into the realm of all-round audio system.
All of that for £160, with free UK delivery.