We also do both short verses and longer passages, and I try to provide the background information for the verse on the first day we begin with the memorization.
Because the Catholic Church has a schedule of the readings for each weekend, I am able to pick verses or passage that we will hear Sunday at mass, and that is a big help with providing context (and further explanation because the passage is likely to be talked about in the priest’s homily). It’s become our “thing” at mass – when the memory verse comes up the kids wink at me or give me a smile or a high-five. When my younger ones were toddlers they would say (usually in a loud voice), “We know this one, Momma!”
The Church’s reading cycle is three years, and we’ve been doing memory verses for two years, so next year at this time the kids will know at least one passage each Sunday!