I main heals and Monk is one of my favorites. He provides a great mixture of mobility, sustain, damage, and support.

Build 1: QM DPS
This build, as the title suggests, is pure damage. I think this is more of a quick-match build in which you'd like to play monk as an assassin. Pair radiant dash with deadly reach during battle for this build.

Build 2: HL DPS & Heals
This is the build that I've been using in Hero League (rank 1) and it is a BEAST. I've been matching Rehgar in heal numbers (~100k healing) while also pumping out ~60k damage in 20 minutes. Epiphany isn't consider one of his favored talents at 20; however, with this build it is perfect. At level 20, you can launch volleys (via radiant dash) 5x on one hero and finish with seven sided strike. In general though, I like to open with seven sided strike and follow up with my 3 radiant dashes on one target, hit epiphany, then hit 2 more dashes on the same target. This does the trick on most assassins.

Build 3: HL Pure Heals
This is the build that I used to use (until I started using my build detailed in Build 2) and it provides amazing heal potential. You'll need to be good with Divine Palm. If you can't hit Palm, take seven sided instead.