Western Europe: British Isles, France, Low countries, Iberia, Italy
Other than Ireland and northern Scotland, the lands covered in this description were under Roman rule from the 1st Century to 5th Century (some later), and hence some inhabitants of these areas could theoretically come from ANYWHERE in the Roman world.
Also Note: not all migrants settled in great numbers at any particular region, but nonetheless probably contributed genes in these regions. The Huns (a central Asian people), for instance, charged across Europe and western Asia in the 300-400s. So in fact we can't cover all the possible lines from which our particular ancestors might come.
Ireland: Inhabited by the "native" Irish Celts for pretty much the whole interval we're covering. If from Dublin, Norse (Denmark and Sweden) populations since c. 900, so see Scandanavia for earlier times.
*Scottish: The Scoti were Irish raiders who arrived in northern Britain c. 500; local Britons were present through the whole interval we're covering. In eastern Scotland, Norse (Denmark and Sweden) invaders at c. 900 *Cornish: Native Britons in Cornwall were present through the whole interval we're covering; English migration in c. 500-600 A.D. (so see English)
*Welsh: Native Britons in Wales since c. 600 B.C. *English: Native Britons were present through the whole interval we're covering; Angles, Saxons & Jutes (from coastal Germany & Denmark) invade c. 500 A.D.; Danish conquest of eastern-central England (the Danelaw) c. 700 A.D.; Norman (Francified Danes living in Normandy) invade in 1066 A.D. Iberia:
*Basque: Present in the Pyrenees region from extremely ancient time
*Portuguese, Spanish, Catalan, etc.: Native Iberians were present through the whole interval we're covering; Vandals (from Denmark) and Visigoths (from Danube River Delta) invade in 409; northern African and Arab Muslim forces ("Moors") conquer Spain in 756 A.D.; Expulsion of all non-converted Muslims and Jews after "Reconquista" in 1492 A.D.
France: Gaulish Celts from before the time we're examining; Franks (loose confederation of Germanic tribes from Rhine River region) invade via Netherlands and Belgium in 400s; Britons (later Bretons) settle in what is now Brittany around same time; Burgundians from Eastern Germany in 544 A.D.; Normans (Danes) settle in Normandy in 911 A.D.
Italy: Italian tribes since before the interval we're covering; Greeks in Sicily since before the interval we're covering; Ostrogoths (from Danube River delta) invade in 450s; Lombards (from Sweden) settle in northern Italy ("Lombardy) in 500s; Arabs conquer Sicily in 827 A.D.; Normans (Danes) slowly conquer Sicily from 1062-1091
The Low Countries (Belgium, the Netherlands, Luxemburg): Native Celtic tribes since before the time covered in the assignment; invasion by Franks (loose confederation of Germanic tribes from Rhine River region) in early 400s A.D. Wallonia was French-speaking, while the rest were Germanic-speaking (Flemish, Dutch, etc.), but all are Celtic & Germanic ancestry.