I think, after much consideration, I'll go with a monk. I already know that paladins and rogues are pretty amazing in 5e, so I think I'll give the monk a try and see how well it holds up compared to its 3.5/Pathfinder cousins.
So now the question is: what type of monk should I play? And what race? Since I start at 6th level, I'll have an ASI available. Would a feat be more beneficial than increasing a stat?
Given that Monks aren't big on the armor or shield stuff, nor polearms, I suspect not--most of the best feats belong to those categories, or at least the feats everyone raves about. With two 17s, you're delightfully close to capped stats, and could actually max one out if you play a race that gets an appropriate +2.
As for type of monk, your stated party and interests suggest either Open Hand or Shadow.
Open Hand has self-healing (useful when you're the only one who wants to get anywhere near enemies), some crowd-control effects, and eventually gets Quivering Palm which really messes enemies up.
Shadow has stealth, the amazing shadowy teleportation, and if you exploit your shadow effects enough, can become Invisible on a regular basis. It wouldn't perfectly synergize with your party (you have humans, and might wish to play a human, and a Light cleric means bright lights!) but it would help mitigate the "I'm the only melee guy" aspect.
In fact, instead of listening to me, just hit up
this guide I found. It'll be faster that way, and you can make your own decisions.