Twofish vs. Serpent vs. AES (or a combo) I've seen some posts and info online, but they are from 2009, 2010, 2011 or 2012, which is 3-6 years ago, which is a very long time. So I'm looking for an up-to-date answer about which of these is the safest encryption to be used, or rather most unbreakable? Particularly interested in encryption programs, so performance would also interest me, not only security.

I think things have changed since Snowden's postings, though then again - I know that a file encrypted with some sort of TrueCrypt algorithms remains uncracked after a few years of trying in the FBI.

So, having that in mind, I'd like to know more about it all so that I would be able to choose the right algorithm for me.
None of Twofish, Serpent and AES are currently known as broken, so as far as security is concerned, you can use any of them. AES has a slight advantage because it's very widely used, so if it gets broken you're more likely to hear about it and get relevant software updates quickly.
The Snowden postings haven't changed much as far as cryptography usage is concerned. They confirmed what was generally suspected before, which is that the generally-accepted cryptographic primitives are safe even from NSA-level adversaries¹; it's the systems and sometimes the protocols that are insecure. What's important is not your choice of primitive (as long as it's one of the generally-accepted ones, e.g. one approved by a NIST standard), but your choice of software.
AES has the advantage that high-end x86 and ARM CPUs include hardware acceleration for it.
If you're a user of cryptography, as opposed to an implementer of software like GPG, keep in mind that if you're typing the letters A-E-S into your code, you're doing it wrong.
¹  You might consider Dual_EC_DRBG to be an exception, but few people used it because it had no obvious security benefit, and its potential to be backdoored was known, and it was slow.