Point size chosen depends on a number of critical factors:
For printing, anything less than 12pt may be very difficult to read. Thus, if you are providing a PDF file, assume that it may be printed. Furthermore, most screens and PDF viewers are set such that 12pt type will be readily readable.
The actual design of a font affects its readability at a particular point size. San serif fonts (Helvetica, Arial, etc.) may allow a smaller point size (perhaps 10pt as opposed to 12pt). Some complex serif designs may require a larger point size (perhaps 14pt as opposed to 12pt) for reasonable readability.
In addition to the actual point size, consider the interline spacing issue as well. Contrary to what the defaults may be in Microsoft Word, you should allow at least 1.2x the point size of the text for what is known as “leading.” Thus, in Word, if you set the text point size to 12pt, set the line spacing to Multiple at 1.2. For 12pt text, that provides leading of 14.4pt. Also make sure that you have adequate inter-paragraph spacing. Depending upon your tastes and the font chosen, such inter-paragraph spacing may be between 0.5 to 1 times the leading of the text; for 12pt type with 14.4pt leading, the inter-paragraph spacing might be between 7.2pt and 14.4pt.
Readability is critical. You might want to err on the side of allowing enough “white space” as opposed to shoving more on a page.
All this points back to the advice give prior the previous poster and to which I and most others subscribe to in terms of résumé writing. Keep the document as short and concise as possible. You don't need to detail every aspect of your career and academic background. Choose the highlights of your recent achievements and your goals. Everything else works against you. What you want to achieve is to pique their interest such that you receive an interview, not to burden them with War and Peace!
- Dov