There is no Paradox in Terminator.
The first you have to take the evidence of chaos theory and that all things are interconnected.
The first timeline we have to look at; is the timeline of the unknown father. This unknown father is of John Conner's original father. Who died before the war or during the war. We don't know who this father is, however he must have existed for John Conner to be born. Thus allowing Johns existence, and for the war to happen, and for him to send Kyle back.
The photo of Sarah in the car; which was gives to Kyle could have been taken by the original father, who we don't see as he is taking the picture. The paradox is cleared up once the time travel element is introduced; the photo is not taken by the father but by a child. It’s just chaos theory that Kyle has the photo and falls in love with Sarah. The photo was clearly given to Kyle before he goes through time, and was destroyed before he goes through time.
In sending Kyle BACK in time John has changed is past, the future paradox is changed immediately, only the knowledge that John has now, is that he must send Kyle back through time; otherwise he wouldn't exist.
The Idea that you can send you own father back in time before you have the knowledge of a time machine is madness! They only find the time machine, after the terminator has gone through.
So did John Conner, have Kyle at his side all the time, hoping to find a time machine so he could create his own father.
It is simple chaos theory; that Kyle is chosen to travel back; he was the wrong person in the wrong place at the right time.
There must have been another father, for time to play out.
The second time line is created once Kyle is sent back in time; and this is the future we are presented in Terminator, Terminator 2 and 3. They know what’s going to happen in the future, the war, skynet, Kyle, time travel and they cant stop any of them from happening; as to do so would create more and more paradoxes.
Also people saying why not send back the T1000 or the TX back in time. The only problem there is, you can't send something back unless you know the out come of the first T800.
Kyle only knows his future, as for him the future has not changed, but for us the future has changed.
The end of T2 states, "The future is unknown; and the only future is, one we make for ourselves".