what does make something inspiring for character when it comes to dnd fantasy races?
wood elves are more or less ranger the race.
who is the cleric, druid or monk the race?
Human, human, and human. Honestly non-human monks make little sense to me.
Clerics are so generic, the only way to make them special is to come up with some really unusual abilities, such as the kuo-tua's lightning blast... which simply becomes part of a domain. The cleric's extra spell-like abilities for clerics became domain spells. I'm not sure what abilities (other than high Wisdom) would make a drow cleric unique. Sure, due to not being tough they tend to go with a casting rather than bashing build, but you could totally build a human cleric that way too.
Druids are somewhere between humans and elves. Given how close elves are to nature you would expect more elven druids, but that conflicts with the "elves make better wizards" vibe as well. Furthermore the only benefit wood elves get to being druids is +1 Wisdom. That is pretty weak. Elves already have the "being close to nature thing" and there's really nothing distinguishing elven druids from non-elven druids.
Of the Wisdom-boosting races, many would
not make good monks, often for flavor reasons. Elves are too weak and fragile, thri-kreen have natural weapons that aren't compatible with being a monk (scratching isn't punching, thri-kreen multiple attacks are not compatible with Flurry of Blows nor should they be, GMs will freak out if thri-kreen are doing a lot of damage per attack, etc), shifters have the same issues as thri-kreen only less so, dwarves are slow and have short limbs... kalashtar would, IMO, make good monks but outside of Eberron you don't see them.