For Tom Waits, I would say Rain Dogs or Swordfishtrombonesis the best place to start. Blue Valentine was the first one I got, so maybe that too.
I wouldn't know where to start to recommend Hip Hop and Jazz to a metal fan.
With Jazz, I would start with the obvious guys Miles Davis, John Coltrane, Oscar Peterson, Duke Ellington etc. Or you go the instrument route, look up some Jazz musician based on a particular instrument. Like for example drums, you'd want Dennis Chambers or Manu Katché, who are two of my favourites and go from there.
For Rap music, you'd want to start with Grandmaster Flash and the Furious Five, Eric B and Rakim, Kool G Rap, Gangstarr, Wu Tang Clan, Pete Rock and CL Smooth, Ty and Talib Kweli among others. Just avoid Jay Z, Kanye West, Soulja Boy and Rick Ross.