I had some lectures of the rules-of-thumb type and nothing stuck for me. It was all jumping across different approximations, implicit assumptions, "use this formula if 5<n<30 and this other one if n>=30", the whole thing felt very ad hoc.
Bayesian formulations and the general didactic style of machine learning texts did the trick for me. By understanding the Bayesian approach, I can see through the frequentist style much better, things don't seem nearly as scary as before.
People treat statistics as some dark art, when its principles are actually quite simple and the applied techniques can be derived nicely by making your assumptions explicit and knowing exactly where and by how much you're approximating and why. You need to go through some simple proofs of how distributions, e.g. Poisson and binomial become normal in the limit.
Maybe different people are different, but for me learning things at a shallow level is quite difficult. It rather works like I either understand it or I'm just memorizing for a test with a very confused and scrambled mental model. The point of "getting it" or grokking it is often quite sudden, not a linear progression through understanding it. If I stop in the middle, I may be able to reproduce the content of a course convincingly, by knowing what I'm supposed to say and regurgitating facts, but not really being convinced of it deep inside.