Fonts with moderate x-heights, not too high and not too low, appear to be more legible, but there are some exceptions, like Iowan Old Style.
There are more subtle aspects that make a font readable, like the size of the serif, length of descenders, and size of apertures and counters.
Similar glyphs should have differentiated characteristics. For instance, the b and d should look different as well as p and q. The j and y should have different descenders.
Generally, the font should have some personality, but too much character can be distracting and cause eyestrain.
Descenders shouldn’t flair so much that they collide with other glyphs.
The font should work when the text is compact, requiring less leading, providing more copy on the page.
The fonts contrast should be balanced with its unique characteristics, but it shouldn’t impose itself on readers. It should feel so natural to read that you no longer notice the design of the font.
Paragraphs should have minimal ragged-right paragraph alignments.
Fonts to study for readability: For screen and print, study Merriweather, Lora, and Source Sans Pro. For mostly screen, study Neuton, Bookerly, and Iowan Old Style and Georgia. For mostly print, study Baskerville, Palatino, and Garamond.