The Migration Period (ca 300-800 AD) was in Europe characterized by wave after wave of of peoples migrating from the north and east and trying to enter the Roman empire, peaceful or by force. Germanics, Slavs, Iranian/Aryan and Mongoloid groups all came, in small tribes or larger federations. Some of the peoples that established themselves within the Roman empire were Saxons, Franks, Langobards, Goths, Vandals and Huns.
The Goths probably started their migration from the south of Sweden, from the area called Götaland and the island of Gotland some time between 300 BC and 100 AD. They slowly made their way south east and ended up by the northern shores of the Black Sea in the late 4th century, on time to be some of the first to be steam rolled by the Huns when they broke out of the eurasian plains. The survivors fled south and begged entry into the Roman Empire in 376 AD. They were admitted, but so mistreated by Roman officials that they soon rebelled. For a long while both before and after this they had an on-again-off-again relationship with the Romans, often raiding, sometimes at war, sometimes enlisting as foederati in the Roman armies. In 378 they won a crushing victory over the Eastern Roman army at Adrianople, killing emperor Valens, and in 410 they sacked Rome after having moved to the Western Roman Empire. Some Goths (Visigoths, the west Goths) ended up setting up a kingdom in Spain and southern France, while others (Ostrogoths, the east Goths) set up theirs in Italy.
There doesn't seem to have been a sharp break between the Roman Empire and the "barbarians", but rather a slow morphing that started with Imperial Rome and ended with a feudal medieval Europe a few hundred years after. The kind of vague continuum that so many people, including some historians, dislike, since it makes it harder to put a label on.

I have started the army by painting up some random old minis I had, as well as some I've cast myself in a Prince August mould. I've also just received some Gripping Beast Saxons and Warlord Games Auxilias, so we'll soon see some plastics here, as well as some Mirliton/Grenadier Steppe Raiders.
I have bought the Hail Caesar book and will probably go for that ruleset, but with slightly smaller units than they recommend.

I do like goth rock, at least the old classics by The Sisters of Mercy, The Cure and The Fields of the Nephilim. The army may end up as another group of Germanics, but I couldn't resist the thread title.