Reddit mentions of A Chemist's Guide to Density Functional Theory, 2nd Edition

Learning programming is good. C++ is always a good language to know (and you more or less get C as a bonus) Structured/Object-Oriented programming languages are all fairly similar (and constitute all the most used ones) Basically it's more important to learn to program than which language, as learning another language is relatively easy once you understand the concepts well. In this day and age, knowing programming is good for anyone in science, anyhow. Some basic course on numerical methods (i.e. solving math problems on computers) would be a good idea too.

As it were, a lot of stuff is still written in Fortran though (in particular in QC), which is rather ancient as far as programming languages go. But it's probably better to learn a modern language before learning Fortran (which, compared to C++ is mostly a subset, akin to C).

Jensen's book (which cyrus linked to) is a pretty good introductory overview of the field. Levine's "Quantum chemistry" is introductory and still relatively broad, but a bit more in-depth book on QC in particular. I'm also partial to Piela's book, which I like for being rather conceptual and descriptive rather than formula-laden. Koch's DFT book is a good one on DFT in particular. Parr and Yang is the polar opposite - very mathematical, but something of a 'bible' for anyone who wants to get into the actual method development side of stuff, although not for the faint-hearted. Szabo and Ostlund is still popular, but IMO dated and not as useful as newer books. It's also relatively mathematical. Helgaker's tome, a more advanced book, is one of few that actually goes into some detail about the computational methods used. (With QC, you could read most of the books above and still be fairly clueless about how to actually write a program to do anything other than the most basic Hartree-Fock calculation)

Although pricey, I liked McQuarrie's book on thermodynamics a lot. It's all you'd need in that area to get you from undergrad to grad level.

If you intend to go into the QC side of theo-chem, learning as much math and quantum as possible is recommended. (although relativistic quantum mech and QFT would be strictly voluntary) How much you'll need depends on what you want to do though; MM/MD methods are theoretically/mathematically a lot simpler than QC methods, and if you're more into 'applied' QC rather than method development, there's less need to know about the fine details, too. But it's good to keep your options open, and lacking the necessary maths skills is certainly a barrier-to-entry for theochem. In particular for those from chemistry backgrounds, who typically have studied less math.

(I was a chemistry undergrad, but I took all the physics students' maths courses. So I can attest to both having had use of most of it, and that it certainly helped me get into grad school.)