Handwritten vs printed assignments
I've seen it done by some students at Utrecht University, while I was a fellow student, and as Master/PhD teaching assistent. I think this was never frowned upon, and personally I'd have a slight preference even for LateX-ed homework, because it is guaranteed to be legible (although I've also seen homework that was poorly LaTeX typeset).
It's pretty hard to imagine any instructor being upset because your submission wasn't handwritten, especially if you're using online submissions as PDFs. Pencil doesn't always scan very well and the cellphone-to-PDF images are worse. I teach EE and I warn my students that if I can't read it, I'm not grading it and I'm not asking a grader to do it, either.
LaTeX is one way to do it but most of my students now type their work (for me and for other instructors) in Microsoft Word using the built-in equation editor. A small number are using the MathType addin (which can generate LaTeX). All of our lab instruments are networked, so if they need an oscilloscope screenshot, they just copy and paste from their browser. If they need a graph or a table analyzing their results, they do it in Excel or Matlab. If they need a schematic, they draw it in SPICE or Multisim. Handwritten submissions are disappearing.
LaTeX is good. No one will object.
Since the industry standard in math is currently some dialect of TeX for producing PDFs, there's certainly no harm in learning how to do this, or in doing it.
Indeed, for upper-division math, certainly for graduate-level math, and absolutely for professional academic math, do not try to get by with whatever kludges "Word" offers. It just does not work as well (at least for the time being... who knows what the future holds?)
Even if one might reasonably claim that details of formatting don't matter too much to actual mathematics... first, they kinda do affect readibility... second, deviation from current standards both impedes readibility and makes one look like an outsider.
In particular, I'd think your instructors would surely tolerate "Word" documents from lower-division undergrads, at some point they'd recommend switching to (La)TeX. To get one's foot in the door, a certain amount of conformity can be helpful, as otherwise-meaningless as it may be.