I think the idea of the Celts originally came from the Keltoi the Greeks talked about, and the Celts that Romans like Caesar talked about: big bruisers of six- and seven-foot warriors (and that's just the women) painted with patterns, wearing kilts, stiffening their hair and dying it blond/e with urine so it looked like a horse's tail, worshipping horse gods in a totemic shamanism, and run by druids who practised human sacrifice, burning prisoners to death in wicker cages.

Later this was taken to mean the group of peoples in Ireland, Cornwall, Wales, the Isle of Man, Brittany and the Basque Country, whose languages (except for Euskadi, the Basque language) are all closely related.

Until the Human Genome boys get their stuff together and are able to work out where we all came from in the first place, tracking genes across the world (if that ever happens) through our DNA, it's all a little theoretical, IMO.