Hi Kid_Electro
Welcome to PF!
I am not as experienced as George Jones and OP on this thread, but I can tell you a few things I've learned recently since I was/am in the same position as you are.
An undergraduate physics course begins with a lot of mathematics (common to science and engineering): series, sequences, limits, continuity, differentiability, integrals, partial derivatives, multiple integrals, complex analysis, Cauchy-Riemann equations and holomorphic functions, Laplace equation, Fourier series (and maybe Fourier Integral), hyperbolic functions, a bit of numerical analysis and statistics thrown in depending on your program. There may be other topics but these are the main ones.
Usually what you do in the pre-final and final years is what shapes your interests or specialization (again program-dependent). If you are interested in sub-atomic physics, then a lot of quantum physics and quantum mechanics is necessary, as with particle physics and nuclear physics (related in some ways). In fact, QM is one of the most important things you'll do in UG-ed. There are four other topics which are equally important: Classical Mechanics, Special Relativity,Statistical Mechanics and Electromagnetic Theory. Usually SR is covered under CM. And CM here refers not only to Newton's Laws and what you may have done in school, but also things like Lagrangian and Hamiltonian dynamics which form an integral part of the curriculum. You will need Lagrangian and Hamiltonian in your study of quantum mechanics, condensed matter and even general relativity.
As for your interest in cosmology, a lot of mathematical grounding goes in before you study General Relativity as a mathematical topic. This shouldn't frighten you as everyone who is interested in GR has to do it to get the hang of the principles and equations mathematically. This includes things like coordinate transformations, four vectors, tensor algebra. But before all that you need to do Classical Electromagnetic Theory including the relativistic electrodynamics. Next comes vectors and tensors in curvilinear coordinates. Now you can jump into GR and on the way get introduced to Cosmology.
You don't have to worry about all that jargon though, because you will automatically realize its relevance and use as you move along.
By the way, (addressed to OP/George), what do cosmologists do nowadays? I mean, is there a different set of cosmologists who work on cosmology without LQG, strings, etc?
After your generalized undergraduate education in physics, you can chose a particular line of attack for your subsequent interests/research. I think when you come out of the univ, you will (ideally) be good at all the fundamental physics that you were taught unless you chose to overspecialize in some fields over others at the undergrad level itself (I don't think this is always possible though).
By the way, I always find mathematical aspects of physics more interesting once I have read the motivation behind them from a popsci book. For instance if you do String Theory and have read Brian Greene's book (or equivalent) you have an overview of the whole thing and when you go through the mathematical details, you can figure out for yourself the motivation behind some coefficient or term. I haven't read String Theory myself (!) but I guess this is a good analogy even for things like QM which tend to get too mathematical if you haven't been doing enough QP (quantum physics)

Feynman's Lectures is an excellent starting point and so are the Berkeley Physics volumes.