I can't help but be reminded of the Legend of Zelda and the timelines created for that--merely because it also shows what I'm beginning to see as an issue of 'compounding naval-gazing timeline plot-hole solutions' that time-travel opens up by virtue of its existence alone. In order to explain the single storyline we see in Terminator, we need to juggle three timelines in our heads. You could probably add more by adjusting things fully for Judgement Day (presumably a timeline exists where the arm was destroyed as well, correct? And yet that's a different timeline than the 'first' (prime?) timeline where Connor becomes important so...)
In essence...Hurray for exponential story complication!
My go-to theory is the opposite of exponential story complication. Any time loop eventually stabilizes after dozens or even hundreds of iterations, until the events of the time travel set in motion the events that will give rise to time travel, and very little further variance happens.
In that first time travel excursion, Skynet might not have had any Terminators to send back. Instead, the infiltrators it used to attack Human settlements were captured Humans with surgically implanted mind control chips, and such an infiltrator was sent back in time. The infiltrator was killed, the control device discovered and delivered to America's military-industrial complex, and the discoveries from that technology accelerated Skynet's development, and enhanced the technology base it started with.
This process compounded, with more advanced technology giving rise to more advanced infiltrators getting sent back in time until the technology involved was simply too far beyond us for the various defense contractors to learn anything else from.
A similar process happened with Sarah Connor. Originally, Skynet's target might not have even been Sarah Connor. The Resistance leader might not have been John Connor. The soldier sent back in time might not have been Kyle Reese.
But Skynet's successful assassination of previous Resistance leaders gave rise to a Resistance leader whose mother was too good at running away and surviving. John Connor might have sent many different soldiers back to save his mother, but Kyle Reese was the first one she fell for, and that bond led to a very strong John Connor who would protect his father until the time was right.
Eventually, this timeline stabilizes on the sequence of events that we saw in the movies, and the time loop is largely unchanged in each iteration. Nobody can escape it, not Skynet, not the Connors, not Kyle Reese, not Uncle Bob.
I guess you could say that the time loop in Terminator is like Sword Logic from Destiny, where the most stable time loop is the one that inevitably gives rise to itself. Patterns give rise to patterns, until each sound is the echo of the last. The only thing that can disrupt the cycle is interruption by outside forces. In other words, the sudden introduction of shitty sequels.