COMICS!!! |OT| June 2017 - AquaBDSM : Sunstone but with dolphins.

Ultimate Spiderman (Peter) the second link is the start of Ultimate line. That link goes through the first Universe shattering (as in start of the fall of the Ultimate line) event. There is a second series between the two links that is still Peter which leads into the Miles link you posted but you have the correct starts for either character.
So I go like this:

1) Ultimate Spider-Man (2000-2009)

2) What is this Ultimate line you refer to?

3) All New Spider-Man (Miles Morales)

And is this Ultimate line an alternate reality and not official?