What's the difference between 나는, 저는 and 내가?
They all mean "I", correct? So I'm assuming there are different circumstances as to when I should or shouldn't use each one.

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I found this really hard to understand at the beginning too, I still don't think I could give a clear explanation of the two, but I think this does quite well:

http://ec.libsyn.com/p/2/9/d/29da01498def6976/ttmik-l1l9.pdf?d13a76d516d9dec20c3d276ce028ed5089ab1ce3dae902ea1d01cf813ed8cb5a46e9&c_id=1552135

if you want to see more from that website, their lessons are free at www.talktomeinkorean.com, it'd really helped me. Hope that helps!

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Yes,they all mean "I"
나 - informal term
저 - more formal term
는 is a topic particle

내가 = 나 + 가
가 is an object particle