I also find that praying the Rosary for a specific intention can bring to mind many reflections on the Mysteries.
For example, if I’m praying for an end to abortion and praying the Joyful Mysteries:
The Annunciation: Mother Mary, pray for those women who have recently discovered they are pregnant that they will choose life for their child in spite of difficult circumstances, just as you did.
The Visitation: Lord, for women experiencing crisis pregnancies, please send people into their lives to help them and support them in difficult circumstances, just as You sent Mary to Elizabeth to comfort and assist her during her pregnancy.
The Birth: Lord, bless all babies born on this day. Help them to find safe and loving homes. We thank you, Lord for all babies given selflessly to other families through adoption. Bless all birthmothers for their great gift of love.
The Presentation: Lord, we present all children to You today – those born, those growing in their mothers’ wombs, those who have passed from stillbirth, miscarriage or abortion. We entrust their souls to Your Divine Line.
The Finding at the Temple: Lord Jesus and Mother Mary, we entrust to you all children who are lost, physically or spiritually, and pray that through your intercession they will be found. May all parents be as devoted as you, Mary, and your chaste spouse Joseph.
Hope this helps!