I don’t think your high school grades or SAT scores are going to matter at all. Retaking the SAT is an undefined operation. Applying to grad school is totally different than applying to undergrad. Graduate admissions are handled within the department - keep in mind you are applying to the department for grad school, not the university. Professors are going to be looking at you not only to see how a good a student you might be, but how helpful a research colleague you may become. In other words, they may want you to be good for something besides sitting in a classroom taking exams.
Get the best grades you can in ME or whatever your major is, and show the best evidence possible of research interest and ability. Many applicants will have perfect GPAs and the MIT ME program is very popular, and loaded with MIT undergrads who seem to have a preference, so you have to find some way to distinguish yourself. MIT is a pretty “hands on” kind of place, so anything you have done to design/build real stuff is probably appealing. If you can get one or more publications in a refereed journal, that’s really great, even if you are second author, which as a student you probably will be. Winning awards is good, too.
I’m sure you know that everyone is admitted first to the master’s program in ME, and you have to make a second cut after that to make it to the Phd level.
The GRE is required, but I don’t think it is a hugely significant factor in admissions. Even though the ME department says it does not keep statistics on GRE scores, most/many applicants will have high scores, so if you are 'way down low with the score and not an outstanding applicant in some other way it might hurt you. If you have a high math GRE and a so-so verbal you are probably in fine shape.
I do not know how helpful co-op or job experience would be. If you really want to go to grad school I would not recommend putting off applying in order to work for a while. Engineering grad school is not like an MBA program in which they want to see several years of work experience. Also, in my experience, the longer you pull down a good salary in a job, the less likely you are to want to go back to school. Also, especially if you are planning to go for a Phd after the master’s, the skills you will need to do well in the qualifying exams will fade with time.
IMHO the best thing you could do is get very well acquainted with at least one faculty member in your department who is likely to be considered a leader in his field by your target department at MIT, work for him or her, do a great job, then get a solid recommendation letter and better yet a phone call to a colleague at MIT to give them a heads up that you are applying and ought to be strongly considered. Given that you are coming into UF as a junior and don’t know anyone yet, you will have to work hard and fast to get connected with a faculty mentor.
Financial aid for graduate school is very different from undergrad, so I recommend you research that, also, especially since you alluded to financial concerns in your post.
Finally, there are lots of fine engineering graduate programs, and your selection of grad school will depend very much on whether you are aiming for an industrial or research career, what degree level you want to achieve, and very importantly, exactly what subset of mechanical or aerospace engineering you want to specialize in. Undergrads are expected to spend some of their time figuring out what they want to do when they grow up, but by the time you apply to grad school you are supposed to have figured that out with some specificity. MIT is a great place, but there are lots of great places, and many may be even greater depending upon what you want to do professionally.
I was an undergrad and grad student in ME at MIT a long time ago, but I have kept more or less current, and I think what I have told you still represents the current state of affairs; however, caveat lector! One thing I am sure of: talk with several of your professors at UF and develop a close collaboration with one or two of them. Not only will it help your grad school prospects, but you will learn a lot and have a lot more fun.