You don’t need to read “A Fire Upon the Deep” first… the stories are more or less unrelated except for setting. (There is one character who is sort of in both, but going into detail about what that means would spoil it too much).
Both are excellent and worth the time. Skip the other Vinge books until you are sure you want to read everything he wrote, they are “merely” 8/10 instead of 10/10.
Vinge was a CS professor who really made sure everything “fit” together in his works. Although “A Fire Upon the Deep”, started in the late 80s and published in 1992, posits that civilizations much more advanced and capable than ours would be communicating primarily through something like Usenet, which feels a little quaint.
NB that Vinge was the one who popularized the concept of “the technological Singularity”. His books have interesting authors notes where he talks about coming up with ways to write about a far future when he believes that the Singularity is right on track for 2050-2100.