This and "Rapper's Delight" by Sugarhill Gang are milestone singles to know, as well as "F*@$ tha Police" by NWA. Grandmaster Flash is probably the first big name MC to break, with Kurtis Blow to follow. (Even Blondie got in on the act.)
The album to hear is really Fear of a Black Planet or It Takes a Nation of Millions to Hold Us Back , both by Public Enemy; that was perhaps the most seminal work of the day, lyrically. It speaks to a lot things still yet unspoken in newly integrating America.
"T.R.O.Y." is a favorite single, and Jay-Z and Snoop are MCs I like, though Mos Def is the more complete musician. Erik B. and Rakim are worth checking out. KRS-One is widely respected for his literacy, though some rather marginalized theories pop up behind his lyrics as well as Mos Def's. DMX is another master of the genre.
LL Cool J, 3rd Base and the Digital Underground and the New Jack Swing movement (Big Daddy Kane, Heavy D & the Boys) were the rage when I was coming up. The big pop sensation was the Fat Boys, a kind of comedy thing, starring the Human Beat Box. 2 Live Crew was the kind of vulgarity teenage boys like to pass around, if for nothing else but the lewdness. Willis Woods was working with Mark Chubb and Chad Owen at my school; they were the closest thing to a fully functioning band at Model High School, so I can't leave them out. The arts weren't something nearly as mainstream as sports and fighting and cars.
Run-DMC is how most white kids my age learned about rap, and if you're a little younger, it might've been Young MC or even...MC Hammer, who owed his groove to Rick James. He got ate up by the wave represented by Ice Cube: Gangsta Rap. Somehow, I almost left out the one band that gets lots of alt-rock play, the rap group that hit big in the wake of Run D.M.C.'s "Walk This Way" and never looked back: The Beastie Boys. The critic's choice there is usually Paul's Boutique, but I've yet to get that one and really enjoyed the follow-up with "Sabotage" and about half a dozen radio cuts.
Tupac and Biggie are worth checking out for their technique, and if you want to hear about a different way of life Tupac and Dre and his proteges are great. Some people really love Eminem, but he took a few records to grow on me; I was looking for something besides anger issues at the time, but his facility with words was undeniable. I'm very ticked off, but I live laid back and in all the peace the world will allow.
It wouldn't be right for me to forget Missy Elliot, nor even Salt-n-Pepa, but the woman who was way, way ahead of her time was Neneh Cherry. Her few top 40 hits don't do justice to her inventiveness.
Once you get to Neneh, you reach a crossroads with whole other types of sounds, like Soul II Soul, De La Soul, Sade, or Swing Out Sister, predecessors of a new soul coming out of Britain over the 90s, like Portishead.
That crossover songwriting appeal stands out in my favorite act to come out of the Dirty South: Outkast. Although "Ms. Jackson" and their album Stankonia was their buzz breakthrough, their monster commercial hit was the 2003 double album Speakerboxx/ The Love Below.
I didn't get off at first listen to M.I.A. and I'm actually full of questions about the Sri Lankan politics, as I have two actual Sri Lankans with sophisticated views of the country as reference, but sometimes, as with Kanye West, the production and the musical package as a whole might supercede someone's frustration with the lyrics or the public persona. There are many more political and socially conscious hip hop acts out there, but why not explore?
Finally, you'll find another category of musicians living in samples, which can come from anywhere. Parliament Funkadelic, Sly and the Family Stone, Curtis Mayfield and James Brown are probably the most commonly sampled groups of all time, along with many Stax artists, the Ohio Players, and Miles Davis.
I have probably met more aspiring rappers than any other type of professional musician. I would have to reach back a bit to come up with names, especially since some record labels and ideas have been duplicated since then (I met a rapper whose cd was called Dirty South back in 1998).