[kachnuv_ocasek]

Same background here. I finally got into stochastic calculus last year thanks to a local college course (after several unsuccessful attempts on my own).

You need at least

1. a basic grasp of classical calculus, measure theory and topology

2. solid understanding of probability theory

3. basics of stochastic processes

I believe you should be able to dive in from there. It's good to have an idea where you're heading as well (mathematical finance and modelling and pricing derivatives? Bayesian inference and MCMC? statistical physics?).