Which files do you recommend I start with to learn Bitcoin? In the bitcoin/src, which files are the "main" files I should start with if I want to learn how Bitcoin works? In other words, where's it good to branch off from?

I'm new to C++, but can code okay in PHP and Python. I'm learning C++ along the way.
I certainly appreciate your level of enthusiasm to want to dig straight into the code, but if I were you I'd start with the Developer Guide on bitcoin.org, and perhaps also the Developer Reference. A whole lot of effort has gone into this documentation (especially thanks to this guy), and I think you'd be remiss to not to take advantage of it.

After digesting some of that content, you'll have a better idea of what particular aspect of Bitcoin Core interests you the most. As I'm sure you've noticed, it's a rather large codebase, covering consensus issues, blockchain/storage/pruning issues, elliptic curve cryptography, DOS issues, Bitcoin scripting issues, Bloom filters, wallet issues, UI issues, and tons of other things I can't begin to fathom. After getting a good technical overview of Bitcoin and posing a more specific question, I'm sure someone (perhaps not me) can give you a more specific staring point.