Well, one thing that the sequels basically ignore or forget is that originally Skynet turned on humanity because it thought we were attacking it. The technicians at NORAD didn't know that Skynet had become self-aware, thought it was malfunctioning, and tried to shut it down so they could figure out what went wrong. Skynet perceived it as an attack and went scorched earth. Literally.
Obviously it had access to more than just missiles or it never would have been able to build the robot army it uses, but as a product of the times the early stuff was made it was also probably a centralized position.
This matters because, well, if Skynet never turns on humanity then we'd be dealing with this original incarnation of Skynet rather than the later incarnations that came about as a result of Skynet being born at different times. (Decades later in the case of Terminator 3.)
As for the effects? I guess it depends on why Skynet didn't turn. Either the technicians managed to shut it down before it could launch any nukes, or they figured out it was self-aware before a misunderstanding caused so much death and destruction.
Yup! The sequels ignored that Skynet's original incarnation going hostile was a mistake (according to the director, once it realized what had happened, it was horrified and racked by guilt, but couldn't self-terminate: the Resistance was basically suicide by cop, but it had to do its best (or as best as it could to satisfy its programming at a minimum level) to win.
The second incarnation, from Judgement Day, reacted out of self-defence -- disproportionate, sure, but it wasn't actively malicious at the start.
By Rise of the Machines, this version of Skynet, from Cyber-Research Systems, was actively malevolent from the get-go: maybe it weren't
originally, but after becoming self-aware and learning in the background and realizing that humans would go ape-shit on it (or perhaps learning of its possible progenitors' demises due to timeline contamination) it decided "them or me -- I choose me!". Either that, or CRS' programming over Cyberdyne's were more aggressive.
1's Skynet was a computer that had everything plugged into it (e.g. like a PC peripheral, like a mouse and keyboard); 2's was an intelligence that had everything networked
into it (like a master computer and slave computers under its control); 3's was a decentralized intelligence across millions of computers; Salvation's was presumably still 3's, though self-developed to being more cloud-like as a natural progression; Chronicles' was much like 3 and Salvation's, albeit earlier and online in the modern day, lurking in the background; Genisys' was the most advanced yet, being pretty much a Cortana-level of AI without having been created from cloned or pre-existing brain-meat.
Oh, and then there's Legion, a discount Skynet from a terrible, Chinese knock-off sequel, but we don't talk about that or its film.