Yeah, population genetics and language are only loosely connected. As you well know, the Hungarians might speak a language with roots far removed from most in Europe, but they're genetically indistinguishable from their neighbors. There's been little large scale population replacement since the Indo-Europeans first came in from the steppe.
I mean, you're basically right. There were the Ice Age hunter gatherers, who expanded from Spain to the Urals once the glaciers receded. There were the first farmers who came into the continent (who appear to be the origin of the genes that fix skin color in most "white people) from Anatolia. And there were the Indo-Europeans. The PIE, though, appear themselves to have been a hybrid of the North Eurasian hunter gatherers, who were genetically different from the West European ones with gene flow from North Asia, and another Middle Eastern group that arrived onto the steppes from over the Caucasus. The North Eurasian group, that can be broadly associated with Uralic peoples, is really interesting in the sense that there are people in Scandinavia today who might be blonde and speak a Germanic language like Swedish or Norwegian, and yet have certain genetic traits that have more in common with Chinese people than they do the rest of Europe.
Thanks, btw. This is one of those subjects I rarely get to geek out on.
Edited to add a piece I apparently left out.