Alrighty, so I have a bit of a love-hate relationship with Dan Carlin, but the fact that he's made you eager to go deeper means that something's definitely going right! The good news? There are a significant number of biographies on the ban, but my favourite to recommend - especially to those who just finished with that podcast - is Goldsworthy's Caesar: Life of a Colossus. It'll help you to iron out some of the inaccuracies, speculations, and wild theories thrown out by Carlin and gives you some solid context on the world of the Late Republic. Goldsworthy's pretty good with citing his sources in that book (and the two subsequent biographies, which cover Antony and Cleopatra and Augustus - both of which are superb if you want to continue the story), which means that, if you have a particular question on a specific point, you can flip to his endnotes and see where he got something from and why he says what he does.

That book (or trilogy, if you read the next two as well) can easily sate a huge chunk of your curiosity on the ancient world, especially if you're focusing on Julius Caesar. If you'd like to read more, I can certainly suggest other books around that time period, especially because if you just look at the first century, you only have a glimpse of one of the most chaotic periods in Roman history ;)

I would suggest Caesar's own the 'Gallic Wars' and the 'Civil War'. I haven't read the 'Civil War' yet, but his commentary on the Gallic wars is pretty good.