In the examples below, the writing is not only more accurate but stronger if you omit those expressions.
* Jana began to move around the area. (Jana moved. . . )
* I have begun to include singing or listening to inspirational music (I include singing. . .)
* The poetry of Edgar Allan Poe began to take on new meaning. (The poetry of Edgar Allan Poe took. . . )
Unless I mean interrupted activity,
I'll avoid using started to, and began to.