Mid fantasy, but not Tolkien fantasy. The fantastical elements revolve mainly around what scholars call Enigmas, and fully understanding these. Magic will require both studying and pondering said Enigmas, so basically mages are natural philosophers. How you discover them and what they do... Well they're called Enigmas for a reason ;) 
(PM for more info, only mage characters should know anything else)

I haven't considered fantasy races yet, but I don't want Elves, Dwarves, Trolls, Orcs, Goblins, Hobbits, etc., because they're kinda used as a crutch in my opinion.

Overall, everyone has the capacity to do magic, but because of the education, study, and mindset required, it's fairly rare. On average, about 1 in 100 people know a low tier spell, 1 in 250 have 5 or 6 spells at a middling power, and 1 in 1000 are as powerful as what we'd call a mage, with tens of spells at their disposal, some possibly taking days to complete.

[@rush99999]