Upcoming Engineering Senior... what are the options?

My background, for context: MechE rising senior at a small (laughably non-target) WNY engineering school with business and math minors, 3.7 gpa, became interested in finance last year. I have accounting, finance and investing knowledge and have done a lot of self-teaching and research. For experience, I was an undergrad IP law clerk last summer and am finishing up an engineering internship this summer. My only financial connection is a prof who was formerly a VP at the NYSE, but he has been teaching since mid 00s and not sure how willing he would be to pull some strings if he knew someone that could help me. I need to make a decision: go the legal route, go into engineering then possibly into finance, or try to go straight into finance.

My questions: If I were to go into finance (be it IB, PE, Corporate, funds), what would be the best course of action for me to take for each industry? Try to break in straight after undergrad (unlikely at this point?), work as an engineer then crossover, or grad school (this brings up more: grad school right away or after working a few years? MBA vs MS Finance?)

Sorry for the short novel, my prof's hard to reach over the summer so I came here to ask. I know this is a lot of very broad questions, so any useful info/advice/personal experiences at all are much appreciated. Thanks!