Re: PCA vs. tSNE. I don't know much about tSNE, but if it is a "manifold learning method" as the sklearn docs say, you could try something like LTSA instead:
Then, it's not difficult to understand what a manifold is, but it took me a number of attempts to get it, and then I only did when studying them formally with Spivak 1963. Now the concept of manifold seems patently obvious to me and not really needing much formalization, but...
e.g. http://www.aaai.org/ocs/index.php/aaai/aaai11/paper/download...
Then, it's not difficult to understand what a manifold is, but it took me a number of attempts to get it, and then I only did when studying them formally with Spivak 1963. Now the concept of manifold seems patently obvious to me and not really needing much formalization, but...