MOPS is Mothers of Preschoolers. My church has lots of young families and a huge MOPS group. I love that you are involving adults in reading to children--many kids don't live near grandparents. Adults need to model reading for children, especially when children have so many electronics competing for their attention.
A basic description and links to resources I have used can be found here. I have done a separate "read-to-me club" for preschoolers in the past. This can be great if you promote it at MOPS or other preschool events.
Prizes/incentives can be divided into age-appropriate groupings if you are covering preteens as well as preschoolers. I look for sales on colorful Bibles and other gift items year round and save them for summer reading prizes.