Amp - something old but not classic off eBay is appealing, but a £80 single input chip amp from Amazon will be fine, if inputs grow get a switch box. I generally point people towards Q-Acoustics for cheapo speakers, but I'm sure there are others. An afternoon at your local Richer sounds would be fun.
The rest of the budget then goes into the turntable. Rega Planar 1 with built in MM stage and the decent Carbon MM cartridge (maybe other bundle deals out there) would do a fine job, and last him until he's earning enough to better it.
You will have some budget left - spend that on records that nowadays are very expensive and of atrocious quality. My step-daughter sells off her old vinyl on eBay to finance her latest enthusiasm.
Before you start, get him to build a RPi with an Amp hat, and a pair of speakers, costs peanuts and maybe won't quite do what the Rega would do, but add in a year of Tidal or Quobuz and he's got access to (nearly) all the music in the world and the start of a fantastic journey.