I have worked in algorithmic trading, hedge funds, and investment banking. I have degrees in CS and Mathematics.
There are a rare few people who have walked these footsteps - see Jim Simon of Renaissance or Doyne Farmer of Prediction Company. And of course there are more you never hear of because they don't have enough money or interest to garner media attention. This community is not an open community because unlike the open source world, it is not beneficial to share knowledge. Governments have to force them to.
One question I wonder if you've considered: do you feel comfortable working within boundaries that governments have the power to change? It's an aspect of the job I find interesting, but I feel many members here would find frustrating.
Mathematics is far more important than C.S. at crafting algorithmic trading strategies, but developers are in far more demand. Quant shops only really need one genius, and maybe a few in training in case the first gets hit by a bus.
In terms of what mathematics: you're going to need stochastic calculus, but don't worry about that yet. Unless you are blessed you're going to need a PhD in math or physics. The importance isn't the thesis, but the topical knowledge along the way regarding which relationships break down under what conditions. Most entry-level quants go for the PhD and pick up stochastic calc while job searching. Machine learning is no panacea: regression (a form of machine learning) is the oldest trick in the book.
So I'd suggest forgetting about finance altogether until you absolutely have to. If you're absolutely serious: ride the academic train for as long as you can. It's not easy riches, but neither is quant finance. Easy riches is swapping MBO's to your buddies on comission.