Future Math PhD Looking to get into Hedge Fund

Hi, I am a Applied Math PhD student. My research is in CFD and solid mechanics applied to physiological problems (very much deterministic modeling). I have some background in Stochastic modeling and parallel computing. I am thinking about what career path I will take when I finish, and working at a hedge fund is something I've been told to look into. I've dabbled a little in economics and finance, so I think I would find it interesting. I've looked into it and read a little, yet do not know too much about it what "working at a Hedge Fund" would entail. Lastly, making a good salary would not be something I would complain about.

My questions are:
-Would I have to make a big career change to pursue a job at a Hedge Fund or any well-suited quantitative and financially orientated job?
-If no, what sorts of jobs should I look into and research?
-What range of pay should I expect with no work experience and a PhD (top 50 UG university in US, top 30 math program... does this affect my outlook)?
-What sorts of steps would make me a better candidate (e.g. reading up, internship, classes)?

Thanks!
(If many of these have been answered, please attach a link)