TX needed to kill kids?

Nobody is saying it made sense. Just offering a possible reason.
Maybe Skynet tried to think logically (I mean we don't even know how it invented time travel, but I'm fairly confident it didn't bang its' head like Doc Brown in Back to the Future). After sending the first Terminator it realized immediately it didn't work because something should have changed immediately (in its'opinion) this is an AI that can think and make millions of decisions in a heartbeat. Sarah then goes off grid, so the target becomes John at a certain point in his life as there are records that Skynet has of his whereabouts at this point in his life (remember most records were destroyed, which is why two other Sarah Connors were terminated). Again, from Skynets perspective the change should have been immediate if the T1000 had been successful. So it sends another TX to target Johns lieutenants because it has no record of where John is since he is now off grid.
Again Skynet is not, as Doc says, thinking fourth dimensionally, it is simply doing what it does.
Of course it could simply be down to wanting to use the same actors as much as possible and sending Terminators constantly to 1984 to kill Sarah Connor would not work as the actress in question would not get away with pretending to be 18 years old in 1991 and certainly not in 2003 when the sequels came about. So it might be less about why Skynet did what it did and more about that.

I gather there must be more time displacement equipment things then because I thought the idea was that the human resistance was winning the war in the future in T1 and this was skynets last attempt - sending terminators back in time, but after the T800 and Reese are sent back it is destroyed.

Having multiple would probably make more sense as it would explain how the TX was also sent years later. I suppose the films never really explained what happened after reese is sent back future wise.

I suppose it also depends on which time travel theory you believe in - if it's a circle or multiple timelines. I do myself believe that probably 1-4 are all a circle - 3 maybe adds issues slightly changing things because of the delay - it's a while since I've seen Salvation but I thought Reese seemed to be the same if not younger - so don't know how it fits because if judgement day happened later then that also changes the future slightly