I used to do Buddhānussaṭi a while back. I basically skimmed through the Viṣhuddimagga instructions, which go into descriptions of nine qualities of the Buddha, and picked out "Arahatō" meaning "awakened, having destroyed all defilements". Buddhānussaṭi produces a wonderful sense of ṣaddhā and gladness. If it is not one's main practice, I believe traditionally it is recommended when one is feeling uninspired to practice. (Viṣhuddimagga mentions some more benefits, among which a sense of fearlessness was something I also found to be true.) In fact, assuming one is a Buddhist, I wonder if it makes a better entry point to meditation, rather than, say Ānāpānasaṭi - which I think is not the easiest to develop (at least in my experience).
"Delighting in existence, O monks, are gods and men; they are attached to existence, they revel in existence. When the Dhamma for the cessation of existence is being preached to them, their minds do not leap towards it, do not get pleased with it, do not get settled in it, do not find confidence in it. That is how, monks, some lag behind."
- It. p 43