I encourage you to use LaTeX for writing up your homework assignments. This is by no means required, but learning LaTeX at this point in your education will be valuable later as you prepare more mathematically-oriented documentation.
LaTeX is not a word processing application. It is a document preparation program. You write an input file, and LaTeX processes the input into a PDF output file, according to specifications you give it. The default specifications are generally fine, but you have a lot of control over spacing, font size, margins, and many other points of style. Your starting point is some "document class" that you specify in the first line of the file.
Once upon a time, you would actually purchase a complete LaTeX distribution for your laptop or desktop computer, but I don't think anyone does that anymore. There are a semi-infinite number of free LaTeX distributions which you might want to consider, or just ask someone who has installed it and see what they like.
LaTeX runs on top of TeX, so you need to install both. See the list of notable distributions and editors from the TeX User's Group for some suggestions. I use a Mac and like TeXShop very much. Another good place for beginners is the online service called Overleaf, which has been gaining popularity over the past few years.
Your first LaTeX document is probably best obtained by copying a working version of something from someone else, and then you can edit it to your needs. (You can use me for that purpose, if you like.) I think the "article" document class is the right thing to work on first.