This was where I was going to take this next. Was wondering who came in first, second etc.
If you're just looking at high-level groupings, there were only two migrations of
Homo sapiens into Europe before historical times: the Cro-Magnon and the Indo-Europeans. If you want lower-level groupings, we ain't got 'em. Since we have no Cro-Magnon DNA, we obviously can't divide the population into tribes and then figure out what order they arrived in.
As for the Indo-European migrations, I've already gone over that. The only people who don't fit into that paradigm are the Basques, whom I've already identified, and the Etruscans, who seem to have arrived in Europe just slightly ahead of the Indo-Europeans and had a civilization going for them to compete with. But we also have no Etruscan DNA, and on top of it, even though they had written language, we have so few samples that we can't decipher it. So we can't figure out where they came from either.
So the various waves, obviously happened over a period of time. It wasn't just like one day all the Indo-Europeans picked up and went to Europe. They must have migrated slowly, and in bands. If my information is correct, the Celts really only survive in modern Ireland no? But at one time, they were all over Europe? As far as the rest of the groups, They pretty much went to certain parts and have remained there yes?
The Celts came first. Having Neolithic technology (agriculture) they easily out-competed the Cro-Magnon. Having lived in proximity to Asian civilizations, they kinda understood the concept of metallurgy, so they even made halting steps to raise Europe into the Bronze Age. And yes, the Celts populated virtually the entire continent--perhaps excluding Scandinavia, but as you know they populated the British Isles except for what is now Scotland, which was inhabited by the Picts, a people we know almost nothing about and--to repeat myself--we've got no DNA and no samples of their language.
The original inhabitants of southern Britannia are called the Brythonic people, a Celtic tribe closely related to the people on Ireland, both of whom were less closely related to any of the Celtic tribes inhabiting the continent. We have enough samples of the various tribes' languages (thanks to the Roman monks who diligently transcribed them using the Roman alphabet) to analyze them linguistically.
When the Roman Empire collapsed and the Roman Legions abandoned Britannia with its overlaid Roman civilization around 400CE, the Germanic tribes sailed over and took charge. We call them the Anglo-Saxons, but there were many other Germanic tribes represented besides the Angles and Saxons. (But the luck of history reminds us of their heritage, in the names of some English counties such as East Anglia and Essex: "East Saxony." Not to mention, the name "England" is just a mosh of "Angle Land.") They marginalized the Brythonic population. The people of Wales and Cornwall managed to hang onto their homelands (Welsh and Cornish are Celtic languages), but the rest of the Celts were either killed, absorbed, or among the refugees who sailed back to the continent and established the region in France which is still called Brittany, and whose people still speak Breton, a Celtic language. Eventually Irish migrants sailed into northern Britannia and although the details are unavailable, when it was all over the Picts were gone and the immigrants became a new people we now call the Scots, whose Celtic Gaelic language is more-or-less intercomprehensible with Irish Gaelic.
Shortly before 0CE, the Germanic tribes came up from Asia and went straight to Scandinavia. Eventually some of them crossed into the main part of Europe, becoming the Germans, Franks and Goths. The Romans conquered them all, but the Germans at least got to keep their language. Speaking of the Romans, we're not quite sure when they arrived in Europe, and there's some speculation that they were just a lost Celtic tribe, but they seem to have arrived a few hundred years after the Hellenic people came around 1000BCE, who established a great civilization and are now called Greeks by everyone except themselves.
And I didn't know that the Balto-Slavs arrived in historical times.
The Slavic tribes were slowly taking over the region that is now Russia, and by around 300CE the Czechs, Poles and other Slavic people established homelands in western Europe.
The Finns, Saami (formerly called "Lapps"), Huns and Magyars were also making their way into central Europe, but they were not Indo-European tribes. The same is probably true of the Bulgars, but they "Slavicized" themselves so thoroughly (adopting Old Slavonic as their language) that today they're included in the ranks of the Slavic nations.
Is there any evidence as to why the Indo-Europeans started migrating into Europe?
The civilizations of Mesopotamia were thriving and their populations were multiplying. The "barbarians" who still lived a Stone Age lifestyle on the edge of civilization had to go. It was getting pretty crowded down there. However, they didn't all go to Europe. That was only the Western Indo-European tribes. The Eastern tribes went east and south and established the civilizations in India, Persia, Armenia, etc. We still neatly divide the language family into Western Indo-European and Eastern Indo-European. The Balts and Slavs are actually Eastern tribes and their languages are much more closely related to Sanskrit and Farsi than to Latin and English.
There were a couple of other Indo-European groups that migrated into places like Anatolia, but they died out. We have useful samples of some of their languages.