This is off the top of my head so I'm not saying I'm 100% right.
Slick rick-the first artist known for storytelling in a fiction type of way with playful made up characters. Also was one of the first artists to have a melody in his flow style that made it sound like he was kind of singing a rap in his verses. This later was extended by Snoop, Lil Wayne and a number of infinite rappers who began pitching their voices in a musical key when delivering their rhymes.
Public enemy-First rap group to try and bring a united movement under black activism. They went back to the neighborhood and schools to encourage Blacks and black rappers to return to their communities and serve them with education and business.
TI- created trap muzik (maybe or at least constantly referred to his music as trap muzik) and first male solo artist form ATL who was considered a legitimate rap artist to go platinum. (Jermaine Dupri wasn’t really considered a rapper. Kilo was a great rapper but I don’t think his albums went platinum)
Run Dmc- one of rap's first rap duo's. Brought a braggadocio rap style of bravado that turned themselves into a trend for marketing, branding Adidas and trying to turn the rap group’s name into a brand itself. Also took efforts to cross over audiences with rock n’ roll. Also was the beginning of the legendary Russell simmons Def Jam.
Def Jam- one of the first rap record companies headed by a black man. It promoted multiple rappers and distributed rap music around the world, started clothing lines, tv programs like Def Comedy Jam which gave Martin, Chris Tucker, Bernie Mac, Bill Bellamy major publicity.
Afrika bambaata-credited for being one of the first rappers period. He was among those who created it and took it from DJ’s spinning records and talking over a beat to the literal art form we know.
Missy Elliott-(I could be wrong) First female rapper dancer to produce many of her own beats, sing complete songs for R&B/New Jack Swing without rapping at all and THEN on the next song rap completely and sing her choruses while investing heavily in creative dance videos.
Ice Cube- the first rapper to use racial slurs constantly against white people when addressing them in his platinum albums. Also was the first to preach, teach and ridicule those who signed with companies THUS making him one of rap’s first proponents of taking ownership of one’s music. Also one of the first rappers to produce and direct highly successful independent movies.
Tupac- created a movement titled "Thug Life". He wanted and talked about taking those in society considered the to be the worst and gave reasons as to why he thought they were great and to be admired. He showed the fear people had of the thugs should be admired as power the thugs had over the world and how if thugs united they could just take over because people would be scared of them. He also was big on being one of the first artists to attempt to shut down other artists physically and business wise. He and Death Row attempted to threaten other groups and Coasts of rap to make it seem that if you weren't with his movement then you shouldn't rap or be allowed to rap. His influence in rap in my lifetime was so big that he single-handedly changed a ton of suburban black kids into thugs and white kids and made almost everyone want to affiliate or be identified as such. He also was one of the first rappers to constantly publicize that everything he said in his rhymes was based on his life and was true. Also one of the first rappers to star in a couple of movies that did well nationally (Juice&Poetic Justice). Also one of the first rappers who seemed to have an infinite number of topics to rap about: from women, to raising kids, black activism, to changing rap flows, to dance music, to gangsta music, to whatever. It's hard to argue, but in my opinion he was one of the first rappers to be a complete solo act package. He wasn't the best at any one aspect of rap, but he embodied almost every aspect of rap at a high level in a way that was better than any other rapper at the time could do all at the same time.
Rakim-Responsible for the flow of rapping that almost all of rap has transitioned to after him. Before him rappers rapped like Run-DMC, Grandmaster Flash and the Furious 5, and after his nonstop rhythmic flow that kept a tone and a breath that seemed to hold verse after verse before taking another breath. He also changed the depths of what was consiered a rhyme in rap, from rapping basic things about what one sees and who one is through their ego to a Rakim based philosophical third person type view on perspective and rhyme schemes where there were rhymes inside of rhymes on each line every time that went inside each listener's mind like a sign of the times. Basically, he single-handedly elevated the rhyme of rap and the thought platform of how to talk about a topic in depth with complex metaphors and analogies. He did for rap what Stevie Wonder did to R&B. And yeah, he was well before my day, but I was young enough to still hear rappers acknowledge his genius.
Master P- first rapper that had every kid thinking they could sell a million tapes out the trunk of their cars in the South. Thus, an abundance of untalented rappers putting out a new sound in the south that could get play in strip clubs. Which this led to a much lower level of content in rap music and a bigger focus on giving that one chorus line chant. Master P known for being his own music distributor and record label from his inception with No Limit rivaling major record labels without any private distributors or record labels backing him. Before him people like Puff Daddy and rappers had been selling their tapes to Dj's but it wasn't the same as how Master P was doing it.