If you’re writing an academic essay or paper to be turned in for grading, use Arial or Times New Roman. And if that’s all you wanted to know, there’s no need to keep reading.

Why Arial and Times New Roman? Because they are basically invisible, they are readable by just about every word-processing program, and they are often expected in writing for school. There are other fonts that meet these requirements almost as well, but why complicate things? Pick TNR or Arial, and you’re good to go.

Just a word of warning, if you google this question you’ll find a hoard of font-nazis telling you to avoid Times New Roman and Arial altogether and at all costs. But their arguments don’t come from a pragmatic place. They talk about readability and aesthetics and and making things stand out. All good arguments, but unless you’re a design major, it’s not what your average teacher or professor is looking for. Arial and TNR are the fonts you use when you don’t want people to notice the fonts you’re using, and this is doubly true when you’re turning in academic work for a grade. Fonts are like so much else in life – if they’re bad, you crash and burn, but if they’re good, or even amazing, you don’t rocket to the top. They can hurt you but they can’t really help you. I have even run across some professors who will actually deduct points for fonts other than TNR or Arial In general, the visual presentation of an essay is effective when it goes unnoticed by the reader. This does not mean it’s unimportant – you should be thoughtful and deliberate about the headings you use, the way paragraphs look on a printed page, how quotations and other elements are set off, and everything else that helps create the visual impression of your essay. You want your essay to look great, visually, but not to call attention to itself. In terms of fonts, this means use what people already know and are comfortable with – Times New Roman or Arial.

Of course if you have strong preferences for another font, or your professor seems to prefer another font, then great, go with that. As long as it’s not Comic Sans or something totally inappropriate, you’ll probably be fine. This post is for people who aren’t font-savvy, have no strong preferences, and just don’t want to spend time thinking about it. TNR or Arial, boom, done.
For those of you who have the time and inclination to fall into the vast rabbit hole of typefaces, there’s an interesting documentary called Helvetica that discusses the ubiquitous rise of the eponymous font, especially in marketing. Just My Type by Simon Garfield is also a great read, combining the history of typography, exploration of aesthetics and design, and much more into a book that is far more engaging than a book about fonts should be. And if you’re looking for more, brainpickings has compiled 10 essential books on typography (I’ve only read Just My Type, so I can’t speak to the others).

I will say that the more you learn about fonts, the more fascinating they become. There is a huge vocabulary of very specific and technical terms to describe the literal appearance of fonts, as well as a bevvy of adjectives like “stately” and “loose” that are used to characterize them.  People who use word processing software as simple tools for writing often don’t think much about fonts, but they are highly designed, highly mathematicized systems that deserve our appreciation. This post on Fabrik has some interesting ideas about the psychological implications of different fonts that feel intuitively correct, though I’m not entirely sure they’re backed by data. And this article from design shack talks about some of the common myths, misconceptions and fake rules about when to use which type of font. 

In my own experience, choosing a font by looking at the font on the screen is like choosing a wine by going wine tasting. After a while, you’re not sure how objective you’re being. You’re not sure how you feel about the next font will be informed by what you thought about the last font. I call this font fatigue, and when it gets bad enough, you get font blindness, where you can’t even properly see the fonts you’re looking at. To avoid this, take breaks, print things out and look at them the next day. 
Or, if that seems like a hassle, stick to Arial and Times New Roman.