Kain Lager-Lowe and Karina Peggau in Albuquerque, N.M., where they looked for a three-bedroom house after a move from Ohio. Gabriela Campos for The New York Times

When Karina Peggau and Kain Lager-Lowe gave themselves a single weekend to find a new house in a city they didn’t know, they went in with open minds, but a few nonnegotiables. First on the list was enough space to accommodate a dog, three cats, 30 plants and 75 pounds of rocks.