I'm also a math grad, and cut my teeth as a quant research/support at an HFT outfit about 12 years ago. My advice is that you start with a bit of industry research; talk to people in the field, look for internships, do whatever you can to find out the quant related skill shortages that are or will be in demand then focus on learning things in those areas. Blindly backtesting, optimizing ("machine learning" lol) historical data isn't going to get you anywhere. Too many guys are doing that, and most fund upper management guys (I'm 1 of those) know it doesn't add much value.