While the Wachowskis may have had plans for the sequels before the first film was made, the first film's development process likely worked against them.
The first Matrix film had approximately five years of development, during which the script changed, notably becoming more and more self-contained and less open ended - note that it was written back when Hollywood believed firmly in standalone movies, rather than serialized films that could launch franchises.
Earlier drafts from 1996 and 1997, which are available on the web, do not feature Neo actually becoming the One at the end of the first movie, signifying that this would've been a development that would take place over the course of the sequels.
Rather, Neo comes back to life after being shot and escapes, leaving Agent Smith alive to fight another day. (In the '96 draft, he even shows him the finger before porting back to the real world.)
Finally, Neo's last phone call suggests he has evolved but not become a God-like being, as in the actual film. He promises the agents that he will 'make some changes' rather than outright show humanity that they live in a false reality, leaving it ambiguous as to what the future will hold.
Most likely then, if the Wachowskis really did have a three-film plan back in the 90s (and note that the creative process is fluid, from script to production to post), then Neo’s journey to fully awaken would’ve been the main focus of the trilogy. So this plan would’ve had to change to accommodate Neo becoming The One at the end of the first film.
The concept of Neo’s predecessors was actually conceived in the context of the first film but was radically different. Early drafts, all the way up to the shooting script, had a subplot, wherein Cipher told Neo that he had 5 predecessors – normal people, whom Morpheus convinced were “The One,” leading them to die fighting an Agent.
Neo later discusses this with Morpheus before they see the Oracle – Morpheus confesses that he misread the prophecy, believing that all he had to do was pick someone – and that person would be the One. He knows Neo is an exception, for Neo sought him out first.
The scene, where Cipher tells Neo about this, was confirmed to have been shot but excised from the final cut in The Art of the Matrix.
This indicates that the Wachowskis never planned for Zion to have been destroyed five or six times prior to Neo’s becoming the One. That is, Neo did not have six Ones before him when the first film was made.
Supporting this is an interview in American Cinematographer Vol. 80 (April 1999), the Wachowskis and Bill Pope firmly state that the film takes place in 2197 and reiterate the backstory provided by Morpheus in the film, which is directly contradicted in the sequels.
My educated guess: in order to get the first film made (its success was not a guarantee), the Wachowskis must’ve needed to make it enclosed and not bank on continuing the story in sequels. So, if the film were a commercial dud, which I’m sure a lot of people expected, it would be a good one-off. Once it became a hit and sequels became a probable reality, the Wachowskis had to open the first film’s plot back up retroactively. Which is why the sequel story is full of holes and contradictions.
Production issues also notably affected the sequels.
The Wachowskis had a falling out with Marcus Chong, who played Tank, over his fee, leading them to write him out. Ostensibly, Tank died off-screen between the two films, even though he was in good condition when last seen in the first movie. [Note that Tank isn’t even mentioned by name in Reloaded, despite being a prominent secondary character in the last film and a more significant one than Dozer.] We can infer from this that the character of Link (Harold Perrineau) had to be created in order to fulfill the role that Tank would’ve originally occupied.
Gloria Foster’s death also necessitated recasting Oracle for Revolutions, meaning that a new subplot had to be created, wherein The Oracle has taken up a different form.
All in all, there is a considerable difference between what is ‘planned’ and what ends up on screen. No matter what Joel Silver and others claims, the sequels, in the form they are in now, were never planned – and they were not written when the first film was released and they, like all movies, evolved during production and editing.