Well, this is going to vary a lot depending on your career goals and field.
Why do you want a master’s in “anything math-related”? There’s a huge difference between mechanical engineering and pure math - there’s even a big difference between mechanical engineering and applied physics. Even within engineering, there are many subfields. What kinds of jobs are you interested in? Are you getting a degree to increase your earning power at your current job/company (in which case where you get it from may not matter as much) or to change careers (in which case it will)?
This is literally a line that I tell my client teams all the time: cheap, good, and quick, pick two. Things that are cheap and good are usually not quick; things that are cheap and quick are usually not good, and things that are good and quick are usually not cheap. Which two are the most important to you?
Cheap and good would be working your way through a part-time master’s program at a local public university in your home state. (Or a second bachelor’s program, which may make sense in engineering.)
Good and quick would be perhaps an executive or online program at a reputable but expensive university (and even then, “quick” means 12-18 months usually).
I don’t really know what cheap and quick would look like. The closest I can think of is one of those online for-profit programs that gives you a lot of credit for “life experience”, but have notoriously bad placement records post graduation; the problem is those usually aren’t cheap, either!
As long as you are under the lifetime limit and you enroll in a degree-granting program at an accredited institution, you shouldn’t have trouble with federal loans. But it depends a lot on your individual situation.