About Rakim we can start by the fact that he released his debut album back at 87.
He was amazing all long 80's and 90's.
I recommend you:
I Know You Got Soul
Know The Ledge
Paid In Full.
Rakim i talk mostly about his discography overall, plus magnificent lyrics.
Paid In Full album was pretty much of an inspiration to some rappers, even for Eminem, as an example, all this shit back at 90's, he also used to sample funk and jazz in his songs usually, used to bring an essence of undergroud hip hop to streets, and, consequently, he also gave us some rappers, i already mentioned Eminem, but i really think that JAY Z took pretty much of his style, though.
About Nas, Illmatic back at 94 was the main inspiration to JAY Z, the biggest hit of JAY-Z'S debut album, "Dead Presidents", samples and interpolates "The World Is Yours", which is, in my opinion, the greatest hip hop song of all time.
Later Nas denied a sample of his(which JAY Z asked) and JAY Z started throwing shots at Nas, indirectly.
After Memphis Bleek in 2000's gave more "heavy shots" JAY Z had came with a diss in 2001, Takeover.
Still, he almost got fucked up, he could have barely had his career ended with "Ether", and i'm not even kidding.
The beef ended in 2005, but, still, Nas has never lost a beef, 50 cent also attacked him and got fucked up.
You wanna know something?
JAY Z was obsessed with Nas, in "Takeover", which was pretty much of a mediocre diss(claims a lot of lies, etc.) which is also a track from 2001, JAY Z claimed Nas discography was trash, but he still would never admit he loved Nas style.
50 cent, on other hand, got fucked up too and some years later he admitted in an interview that his favorite hip hop verse of all time belongs to Nas's "The Message".
Nas released in 96 It Was Written, this album doesn't gets the recognition it deserves.
Nas doesn't has a single bad album, and he was pretty much of an inspiration to Kendrick too, if you don't know.
I will recommend you, in case you don't know:
The World Is Yours
N.Y. State Of Mind
Nas Is Like
It Ain't Hard To Tell
Now, why is he the G.O.A.T.(imo, and of many)
In his debut album he impacted entire hip hop, and he wrote that shit back at when he was fucking 19.
There are also similar cases to Rakim for ex, or Ice Cube.
Imagine, a debut album which is considered the greatest?
Also his lyrics are amazing too, pretty much focused at social problems, sometimes things of our life, such as love, totally concious hip hop motivational, etc.