The two main factors are: legibility at small sizes, and a relatively narrow width, to avoid the syllables affecting the note spacing. And, of course, it has to match (or complement) the font styles of your other text elements -- expressions, tempi, and "page furniture".
Serif fonts are usually considered to be more legible at small sizes than sans fonts. Never use Bold type: a Roman font at a larger size will be more legible and often take up no more space.
Finale Lyrics is essentially "Times New Roman Condensed". If you are using Times for everything else, then it's a better choice than 'straight' Times, which is fairly wide.
(I'd suggest that TNR only ended up on pages of music because it was the 'digital default' for serif type in the 80s.)
Palatino is also quite wide, though it is used by some publishers, such as Faber.
Garamond is lovely, and a classic typeface; though some cuts have very small 'counters' on 'e' and 'a' (the looped bit), making them hard to read at small sizes. Other Humanist faces like Minion Pro, Arno Pro, Adobe Text, Warnock Pro may be better, for a similar style.
Plantin is, I think, the Sibelius default text font, and is OUP's house style. It's quite wide for lyrics, though different cuts and styles are more condensed, such as "News Plantin".
Fonts like Minion Pro come with 'Optical' sizes -- font styles cut for specific sizes; such as "Caption", which is designed to be more legible at small sizes than the standard Roman. If you have these styles, you should use them.
Minion Pro Condensed Caption is ideal for lyrics.
Other fonts that fit the metric criteria include:
Arno Pro (Caption)
Adobe Caslon
(Other Caslons may vary. Apple's "Big Caslon" is not suitable.)
ITC Cheltenham (Book Condensed)
ITC Cushing (Book)
Photina
Kepler (SemiCondensed Caption)
Miller Text
De Vinne Text
New Century Schoolbook is a commonly used in music scores, though again, it's quite wide for lyrics. Other "Centurys" are better, such as Century Old Style, and ITC Century Book or Book Condensed (possibly a little too condensed!).
Avoid fonts like Bodoni, where there is too much contrast between thick and think strokes, with the danger that the thin lines can't be seen when small.
If I may, I have worked on a design for a typeface that emulates type traditionally seen on plate engravings of the 20th century, and it's designed to work excellently with lyrics. It's called Nepomuk. There's an article about it, with links to obtain it, here:
https://www.scoringnotes.com/news/the-n ... tain-type/
(You can download it for free, though contributions are welcome, if you like it!) Apologies for the advert.
Gould suggests that the body height of lyric text should be no less than 1 space, but not much more; though very large or very small staves may need some adjustment to this rule.
