Serif fonts in general are more formal (or "stately"). That's because of the, well, serifs. Sans-serifs visually resemble/evoke handwriting because in handwriting we don't make serifs. Try writing with serifs for everyday stuff and it will quickly reveal to be visually and logistically annoying.

The only question is which brand of formal do you want to evoke. TNR feels very straightforward and no-nonsense to me. So I wouldn't really object to associating it with bureaucratic memos and documents. For something more leisurely I'd go with either Garamond or Georgia. Georgia is my favorite but it's a bit too fancy for long texts. It's better suited for quotes.

As an aside, I hate that Introduction to Algorithms [CORMEN] uses a TNR-like font. It makes it look like a Physics textbook. They could've stayed with default Computer Modern and strengthened my Pavlovian conditioning to it. Whenever I read something in Computer Modern, my heart palpitates a little in the way it did when I sat through my Data Structures exams.