Wep, I'm late. I apologize in advance.

Albanian is an Indo-European language, meaning it's related to all European languages (sans Hungarian, Finnish, Estonian, Basque). We're not sure who exactly the ancestors of Albanians were, but we have narrowed Proto-Albanian Urheimat down to around the Daco-Mysian region, in the Balkans. I'm using Daco-Mysian to refer to the region but is a misnomer because it seems it's implying Albanians as descendant of Daco-Mysians. Maybe they are, maybe they're not, but that region, (in this map Moesia Superior, Dardania) is a safe bet. Any hypothesis beyond that is controversial. Any hypothesis beyond the Balkans is not taken seriously.

This is the current consensus summarized:

It is generally assumed that the early Albanian tribes, facilitated by the collapse of the great Bulgarian empire at the end of the 10th century, began expanding from their mountain homeland in the 11th and 12th centuries where they had lived as nomadic shepherds, initially taking full possession of the northern and central Albanian coast and by the 15th century spreading southward towards what is now southern Albania and into western Macedonia. They first entered the annals of post-classical recorded history in the second half of the 11th century and it is only at this time that we may speak with any degree of certainty about an Albanian people as we know them today, although their predecessors, no doubt with a strong Illyrian element, seem to have inhabited the same northern Albanian mountains since ancient times.

As for the South Slavic people, they descent partly from the people of "barbaric invasion", and partly from local populations: During the so-called "dark" ages, there was a mass migration of people of different backgrounds (Germanic, Slavic, Uralic etc) where they intermingled with the local cultures. Slavic language became predominant in Eastern Europe, substituting many others gradually over time. See this map on Romance Langauges, to get an idea of the population changes. Most Romance languages in the Balkans collapsed, there used to be a dialect continuum from Italy to Romania. Some languages survived, namely Albanian, Greek, Romanian (and related Vlach dialects in the Southern Balkans, and some in the Croatian coast, which are in in extinction risk now).