For engineering, MS would be where I would recommend stopping. You can get entry-level work with a BSME, but that's exactly what it is. Many folks call the BSME a "license to be dangerous."
That said, a MSME can be obtained at a different school than where you did your bachelor's, and can be done a few years after your BS.
Most employers look at your last school, so you could presumably go to A&M for a BS, then, head to MIT for a MS. MIT does have an ocean engineering dept, and the affiliation with Woods Hole oceanographic institute.
I'm currently doing research/engineering for the gov't. I used to teach at a University. Prior to that, I was in the private sector. I also spent a few years in the private sector between my BS & my grad. degrees (I recommend that if you enjoy engineering; the private sector perspective is great!). At the more 'marquee' schools (Ga Tech, Clemson, etc.), there is a good internship program where you can apply for summer jobs with major industrial companies and/or coop programs (1 semester in the private sector) for engineering majors. Clemson, for example, has a tie into BMW (no, you won't get a discount for buying a BMW, but their Mech Eng program is tied to BMW's SC manufacturing plant). (Although an ACT at 30 is at the low end for MIT; the median is probably closer to 32-33 there).
I know the program at U FL (Gainesville; I don't know if that's UF or FS; please don't shoot me
). It's quite good, though like many, you get out of it what you put into it. UNC Charlotte is another of these good, but not well-known programs. Don't forget Va Tech & UT (Texas and Tennessee). I know there are many A&M fans out there, but UT (Texas at Austin) isn't chopped liver for Mech Eng.
The other fairly large issue is the support system and bureaucracy. Smaller schools and private schools (as opposed to state schools) are likely to have less bureaucracy, and a bit more nurturing.
Good luck!