The question of why a T-800 Model-101 (Arnie-type) Terminator was chosen is different in each of the films.
The T-800 in this film is a top-of-the-line model. It's literally the acme of what Skynet can produce and while there are indeed other models seen (particularly in the flashback sequence), the Arnie version is likely the most lifelike out of the bunch.
REESE: Pay attention. The 600 series had rubber skin. We spotted them easy. But these are new. They look human. Sweat, bad breath,
everything. Very hard to spot. I had to wait 'til he moved on you
before I could zero him.
Terminator: Film Script
Terminator 2: Judgement Day
It's circular, but John Connor chose to send back an identical model to the one that attacked his mother because he (as an adult) remembered being saved by that model as a child
Connor specifically looked for that model to send because he
remembered him as such and wanted to make sure that he's doing what he
was suppose to do - send the T-800 that he remembers back in time to
1995 so he can protect him from the T-1000. He knew that for things to
go the way they are suppose to, he has to find the terminator that
looks like the one that he remembers.
T2FAQ: Interview with James Cameron
Terminator 3: Rise of the Machines
There's no good indication of why Catherine Brewster chose to send back that particular Terminator other than that it may have been the only upgraded T-850 (one with additional infiltration software) that they had immediate access to.
We do know that the 'Arnie' exterior was chosen by Skynet because of John's "emotional attachment" to that particular model. It's not a stretch to imagine that Catherine probably made the same judgement when she was deciding to send him back.
"John Connor was terminated on July fourth, 2032," Terminator said. "I
was selected for the emotional attachment he felt to my model number,
due to his boyhood experiences. This aided in my infiltration."
Terminator: Rise of the Machines - Official Novelisation
Two T-800s are seen in this film, one in the opening sequence (presumably chosen by Skynet for precisely the same reason as in Terminator) and one that was sent back by persons unknown to protect young Sarah Connor. We have no good intel on why this model was chosen (or who it was sent by) but I think we can assume that the fact that it's proven itself to be a reliable protector is a key factor.