From what I can understand, your asking what style of font best characterises the 'ideal' educational institution - respected, safe, knowledgeable.
This is a very personal question as the subject of fonts is a very subjective one with many personal responses pertaining to the context of exposure to various graphical triggers.
Personally, in educational institutions, I view the Serif typeface to be more authoritative, as opposed to Sans. Despite the 'older' look, which many may perceive to symbolise 'lack of progress', the font as a whole invokes a sense of foundation and stability, due to the longevity of its existence.
Times New Roman is one of the most basic and you can delve further from these.
Some pragmatistic examples include many universities, especially the top 8 in America (IVY league) which primarily incorporate these.
A good example of more modern alterations extend to Massachusetts Institute of Technology, who have a badge with the older Serif look, whilst maintaining a modern Sans typeface.