Given the vastness of the Roman Empire at that point, and the military might it could bring to bear, it seems that Gothic leaders such as Radagaisus made a strange decision jumping from the frying pan of Huns to the fire of the Romans. I know much less about Germania’s network of tribes, but I’m certain that their military might would have been orders of magnitude less powerful than that of the Romans - why not go there rather than going after the bully on the block?
Because Goths (and other Germanic tribes of the era) were not interested in fighting Romans and tear the Empire down as some sort of liberation force. What they were interested in was taking advantage of what Rome had to offer in terms of developed economy, infrastructure and the like. They wanted a piece of the pie, so to speak, and their elites wanted to take part in Roman government structure, to serve as commanders, as mercenaries. Of course you had groups that were interested in quick plunder but even those were interested in Rome existing on as without it there would be less plunder. For Goths preferred option when they arrived on Roman borders was to find some sort of accommodation with Rome where they could settle down within Roman Empire and enjoy the protection it offered in return for military service and becoming part of Roman empire. And their leaders understood that they simply couldn't get this in Germania. Their goal was not some sort of new Gothic homeland carved out of Roman empire but rather a place within it. Rome had a history of taking in various groups in such way, what made Goth situation different was the sheer size of them and the fact that these were "people on the move" rather than smaller group composed of adult men.
If you look at Alaric his goal has been to find a place for Goths within Roman empire. Land to settle in, seeds rather than food and so forth. For various reasons that kept getting further and further away causing him to take actions he did. And even in the end he was reluctant to actually sack Rome because he understood that once that is done there are fewer options. Decreasing options and Roman actions caused Goth goals to change in time.
So going to Rome was logical choice because there were better conditions and they could expect better living standards than in underdeveloped Germania and military power of Rome could offer protection against Huns, if some sort of agreement could be reached,
The Goths, Peter Heather, 1998
Empires and Barbarians, Peter Heather, 2009