I can't help it. I do prefer time travel that is into a single immutable past. Anything else is not travel into our past, is it?
Three pure examples of this kind of narrative are:
Of course, in a single immutable timeline, a time traveller can cause past events but there are greater subtleties than that. He can change the significance of past events. He can seem to have changed the course of events, then turn out not to have done. He can learn about an event, then experience it.
In There Will Be Time, the Eyrie recruits a handful of mutant time travellers, including Jack Havig and Boris, in Jerusalem on the Day of the Crucifixion. Much later along his own world-line, Havig, now organizing an anti-Eyrie group, sends Boris to infiltrate the Eyrie by being recruited into it on the same day as his younger self. Neither the younger Havig nor his recruiters suspect the significance of Boris, sent to that time and place by the older Havig.
Niffenegger's Henry DeTamble knows that his ex killed herself on a particular date. Then he learns that it was his involuntary extratemporal arrival in her apartment that triggered her suicide. He asks her the date. He knows what she will do with the gun that she is wielding. He knows that she will not kill him. He avoids saying anything that will motivate her to shoot herself but she does that anyway - on the date on which she had done it.
Similar things happen in The Anubis Gates. Read them all!