Fonts & Character Sets ⇒ Font Style
Font Style
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Font Style
As for broad category, I think any sober "serif" font-face is suitable. I dislike sans-serif or monospace fonts for academic work, except possibly in displays or charts, and of course, calligraphic, cursive or decorative fonts are not appropriate.
I really I think anything from the "serif" section of the LaTeX font catalogue should be fine.
As for particular fonts, I'm rather bored by Times and its derivatives (Nimbus Roman, etc.), but that's not to say that it's unsuitable in general. It's just a personal preference. I like Palatino (e.g., from mathpazo or pxfonts), Garamond (e.g., from Mathdesign), Utopia/Charter (from mathdesign), New Century Schoolbook (e.g., from fouriernc), Linux Libertine (from libertine or xelibertine), and the Kepler Project (from kpfonts) just fine. I go back and forth on Computer/Latin Modern.