So you want to be an astrophysicist? Part 1.75 - should you go to grad school?
Why is there a question? Well, it is several years of your life, earning minimal pay, doing some grind work, including classes (1-2 years at most institutions) and exams (most places have some "admission to candidacy" hoop), with interesting but uncertain career prospects. And you have to do research. Supervised, but independent and original research. Not everyone wants to do that.
You can do stuff with a BSc or MSc, like start to earn money, and still be involved in research. In rare cases you can get promoted through to full professor/senior scientist, and lead major science teams etc, but the odds are bad. So, go to grad school, go for a PhD. It is fun.
We'll deal with the practicalities later. First, what is involved.
Well, learn math. Undergrads tend to be math phobic. Lack of math preparation is the major reason why interested people find themselves unable to go on to astrophysics. Not that you will be a mathematician. Mathematics is a tool, and you need the full kit (there are mathematicians who do physics, mostly in corners of particle theory, or, interestingly, in gravitational physics - relativity or quantum gravity, but physics is not math. Math is tautology, subtle, interesting, useful tautologies [sometimes], physics deals with "reality" with math as a tool of choice).
Now, what is there to do:
1) instrumentation - if you can build bleeding edge, high quality, fragile instruments, go for it. You'll be sought after and hopefully not too under appreciated. If you got the knack, you got the knack.
2) Observations - looking at stuff, using instruments... analysing data, planning observing strategies, and destroying perfectly good theories. There's people who know about that stuff, they can address it. Most astronomers are observers of some flavour (and most observers do some theory too).
3) Theory - are you a physicist doing astro (like astrochemist, or astrobiologist)? Er, well, lets get back to that last one some other time? Or are you and astronomer doing theory? Yes, one of those.
Lots of places don't even have an astronomy department, you're doing a theoretical physics PhD (me!) in an astronomical topic. Even if there is an astro dept, you can still do that. It actually doesn't matter much, it may restrict your choice of advisor a bit, but is usually not critical.
Why? Well, astrophysics covers all of physics (I challenge anyone to come up with a sub-field of physics not relevant to astro). You personally don't have to do it all; your goal after all is to "know less and less about more and more, until you know absolutely everything about nothing". But it is a good start, otherwise how do you know what you're missing.
Astrophysics is data drive, there is lots of high quality data. The quality is progressively improving, and there is no end in sight. Arguably particle theory is now driven by secondary inferences from astronomical data, or astroparticle data, at least until the next generation of colliders comes on line. Why, there's even a subset of cosmologists who are really refugees from particle theory, dabbling in beyond standard model physics (with astronomical implications) and having fun tweaking Lagrangians and seeing what happens.
Sound good? Then go for it.
Next, the practical details (like GRE), and the sub-fields (or some of them). Then, what astrophysicists actually DO. Personally I argue there are several "styles" of theory, and they are complementary. Some people disagree. Their way is it.