But there's some room for variation. Many professors prefer an old-fashioned typewriter-style font such as Courier. It's what's called a fixed-width typeface, meaning every letter takes up the same space: an i and a W both get the same amount. Courier has some advantages over other typefaces: it allows room for markup, and it produces about 250 words on a double-spaced 8.5” x 11” page, so makes word counts easier.
Most other typefaces are proportional, which means each letter gets its own width: compare the width of i and W. Times Roman is a pretty standard default typeface; it's easily readable. Garamond is similar, perhaps a little more ostentatious. Notice that Courier, Times Roman, and Garamond have little “hats” on the tops and bottoms of letters; they're called serifs. Arial, on the other hand — like Helvetica, Swiss, and others — have no serifs; they're called sans-serif faces. Usually serif faces are preferred for academic papers.
Twelve points is the standard size. A point is one seventy-second of an inch, top to bottom, so a twelve-point typeface gives one sixth of an inch to each line. (In fact many word processors add two points — one thirty-sixth of an inch — “leading,” pronounced “ledding,” between lines. But that's getting too technical.) Some typefaces aren't measured in points but by pitch, which is characters per inch, left-to-right. (Note that pitch makes no sense with proportional typefaces, since the width of the characters varies.) The higher the point size, the larger the typeface; the higher the pitch, the smaller the typeface.
But whatever face or size you choose, do give your professors some credit; they're not as stupid as you think they are. They're almost certain to notice if you start playing with fonts to avoid having to write full-length papers. Give 'em a break.