Don't get a fucking Rega! Please!
Kenco, Gerrard, Sonny, Pieoneer, etc they're all good at the right price for the condition. Or not so good at the wrong price for the condition.
Doing up your PL71 would be valid. Starting off with the essentials to get it turning at the right speed. And then maybe not bothering with the arm bearings and rewire and the off boarding - depending.
Just stick the Liar Aygo on whatever turntable you go with.