I have a B.S. in ME, 5 years out of school now. In school I was active in a Christian fellowship and the taekwondo team -- semi-leadership positions in both, and they were both on my resume. I pulled a lot of interview question responses from my experience with taekwondo.
I got my co-op through my school's job placement office, and got my full-time interview from my co-op. Senior year I had my job offer in the fall, which I'll admit meant I coasted the rest of the year pretty hard ;)
I'm currently a program management engineer for Megamegacorp in jet engine aviation (yes THAT one) . I did 2 co-ops with them, so it's the only engineering environment I know. I've been with the company for 5 years now, hired into their rotational program. It allowed me to try working in different areas of the company, and they paid for my Master's degree (also mechE) including one semester of full-time school with full-time pay.
Pros: Some job stability -- airlines are always looking for more efficiency to save a buck. There is no requirement to stay after program completion, so plenty of people leave after getting the free master's. The majority of the people I've worked with are amazing. Pay is not the best but small increases every year with bumps at job transfer and program graduation. Working for a huge company means that there is a variety of positions for engineers - I've worked in technical design roles, in a technical hands-on role (flight test woohoo!), and now project management. We do have engineers at corporate HQ, and there are management vs technical paths available. Travel-intensive positions available.
Cons: There has been one round of layoffs since I've started. I wouldn't describe our environment as cutthroat at all, but aviation is a very cyclical business (lagging behind the general economic cycles somewhat). Benefits are just ok. Overtime is also cyclical, but it is usually paid (straight time)...I've worked over 80 hours/week before but that isn't the norm. Working with the union. Bureaucracy.
We have oil & gas, energy, power & water divisions which I believe have similar rotational programs.
We recently moved to an 'unlimited paid vacation' system which is a pro or con depending on your manager. My current manager doesn't care as long as we get the job done. So by the end of the year I'll have taken over my previously allocated 4 weeks.
My SO works for the same company, but his field of expertise/interest is specific enough that we rarely cross paths and will never be on the same team. He really enjoys his job (major aviation nerd). I'm not thrilled with my job but I'm grinding out a few more years before probably becoming a SAHM.
I would advise thinking about how much OT (paid or unpaid) you would be willing to work and what work environment sounds fulfilling to you (is it important for you to see physical results of your work? Do you enjoy running analyses? How much do you want to interact with people?). Once you start, you can always consider/network with other positions/areas of the company. Look into the possibility of doing cross-functional assignments to learn about different parts of the business and learn about what you like.