Online Alumni Networking

I just finished up my sophomore year in economics at GMU and started a position as an analyst at a government-related firm. However, my end goal would is more so something to do with global data, AM, or trading (I'm open to different paths just one that doesn't involve working for the government....). Unfortunately my school is more of a non/semi-target (we get people from capital one, Deloitte, KPMG, etc.) but for the most part its places like the FDIC, the fed, other government agencies, you get the point (guess that's what I get living next to Washington). Seeing as there's not a lot of opportunities for in-person networking, I wanted to go through our alumni directory and Linkedin to find professionals working in the fields I'm interested in.

My main questions are: is it more acceptable to message them through Linkedin or email, and how to write it in a way that isn't "creepy" I guess lol.

My best template is: stating my name, year, major and university - explaining how my experiences have made me interested in their particular field - asking questions related to their position and experiences within their firm and coming from my university.

I've found that the latter is the hardest to come up with as I don't know how specific I should be with my questions, I just really want to know how they got to their position and what their work is like. I'm trying to figure out where I want to focus my internship/career search in so it's been difficult coming up with specific questions as I don't have much insight to work in the private sector.

Thanks!