There is a third possibility: simple escalation.
As an adult having both grown up with Sarah's stories and having seen what the more advanced cyborgs could do as a child, John would have known that leaving his past-self defenseless against an advanced future weapon would be both dangerous and foolhardy, and that his chances of survival would increase if he sent back some other type of weapon to even the playing field.
"Pops", the T-800 which became Sarah's protector, was simply one off the assembly line...and is a possible alternate universe version of the same T-800 which would eventually have been sent back to protect John himself. So in truth, there are hundreds or maybe even thousands of T-800s with that particular face and body which could have been used. In the second movie, it was stated that that specific unit [we'll say "Pops" for clarification against the others] was "reprogrammed" to be used as a Protector.We have seen humans reprogram Skynet tech of various forms for their own use in Terminator: Salvation. As Kyle is still a teenager, it's clear that this point of the future is set some time before Kyle could father John, so it may simply be that they only had the programming tech necessary to hack an 800 model or below. By the time the T-1000 was deployed, the Resistance may not have been able yet to fully control a liquid metal nano-tech Terminator, but still needed to send some Terminator as a counter measure.
Again, this makes logical sense; sending a human back resulted in Sarah just barely surviving, so obviously something with a bit more power needed to be used. Without wrapping them in human flesh, sending weapons back is impossible, and they'd likely end up in the wrong hands. Sending back a thinking machine which could double as a guardian and a weapon, however, while also being somewhat of an exception to the rule is sensible.
There is another, also likely answer: simple availability.
In most of the future scenes shown in T2, the most numerous and commonly used combat Terminators by far are the T-800; we see them stepping on skulls and massacring hordes of soldiers on a few occasions. Obviously, it was mass produced, so it's likely this is the unit the Resistance had the most opportunity to study to facilitate their reprogramming. From there, it was a simple matter of gaining a fully cyberized version [likely one mass produced with Pops' face], resetting the programming, and sending it out. In hindsight, it might have made more sense to send a T-1000 to defend against a T-1000, but in that film it was stated to be a "new model", so it was either rare at that point, or they hadn't deciphered how to reprogram one yet.
If that was the case, John simply would have gone with what was available.
All subsequent appearances of Pops, however, would then be influenced by John's memories of the specific model; even Pops himself alluded to it being "a face John would trust" in the second film. And in the third film, they were banking on John recognizing his former protector and thus trusting him/it more off the bat. I can't speak to how the latest films may alter that continuity.