The Goths are a persistent figure in the history of the late Roman empire, i've heard a variety of theories as to their place of origin, but I don't know of much evidence. Did they come from the east and Sarmatia, or from the far North? Where did the first "Goths" come from?
The short answer is that we don't know. The 6th century author Iordanes wrote a comprehensive history of the Goths (Getica), drawing on lost earlier sources such as Cassiodorus, and says that the Goths came from Scandanavia. Already in the 6th century CE there were different stories about the origins of the Goths, and Scandanavia seems to have been the one Iordanes favored. However, linguistic analysis puts the Goths in the southern reaches of Germanic territory (see Mańczak, Witold, 1987. “On the Ausgliederung of Germanic languages.” Journal of Indo-European Studies 15, 1-17; ----, 1992. De la préhistoire des peuples indo-européens. Krakow.)
Peter Heather talks about this issue at length (1991. Goths and Romans 332-489. Oxford.) He and others tend to reject the narrative of Iordanes (which is rather difficult to pull off for such a solid source in this time period). It is probably right that they did not make a journey from the Baltic to the Black Sea: it is the "wrong way" as far as Indo-European migrations go, and makes little sense: they would be going from "better" to "worse" in just about every way. It doesn't help that such a migration would have taken them through areas occupied by the early Slavs, who don't seem to stir at all until the Huns come knocking in the 4th c. CE. It is much more likely that the Goths moved south toward the Danube and Roman lands via the Moravian Gate, just as the Slavs would do a couple of centuries later. Once at the frontier, they were presumably halted for a time and had cultural contact with the partially-Romanized Alemannic tribes.
It is even possible that Gothic ethnogenesis occurred right there on the Danube, where West and East Germanic tribes met and mingled, perhaps in Austria, and where they delayed for some time while probing the Danube frontier. From what I understand, this would neatly explain the linguistic evidence, though I'd need help to go into more detail. I know that Gothic has more apparently sharing with Latin and Romance than the other Germanic languages, which seems strange if they originated in Scandinavia. For instance, the Latin suffix -arius is productive, giving Gothic bokareis 'scribe'. For more, the Heather book is probably a good start, but somebody who does late antiquity could direct you better than I can.
I see, the Goths originating just north of the Danube does seem to make the most sense, even if the migration from the North is much more exciting. Thanks!