The biggest assumption that most people have is that the rosary is about Mary. Perhaps this is because we say the Hail Mary more times than we recite any other prayer - in fact, 10 times for every one Our Father. Yet this is deceptive, because in reality the first part of the Hail Mary are taken from the words of the Angel Gabriel as revealed to us in the Gospel of Luke. They are scripture. "Hail Mary, full of grace, the Lord is with you" - Luke 1:28. The second line is also scripture, though this time from Elizabeth. "Blessed are you among women and blessed is the fruit of your womb" - Luke 1: 42. Jesus's name is added as a reminder of who that fruit is and why she is so blessed. The next part is a request to Mary that she aid us in our efforts to reach Heaven by praying for us both right at this moment and at the hour of our death. So, the entire prayer is really a focus on the Incarnation of Jesus and a request for help in growing closer to Him.
Every mystery - with the exception of two of them from the Glorious - is centered around moments from Christ's life and public ministry. The Joyful Mysteries are about Christ's life from his conception through the finding in the temple. The Luminous Mysteries are about Christ's public ministry from his baptism by John the Baptist until his institution of the Eucharist at the Last Supper. The Sorrowful Mysteries are about Christ's last hours from the moment he entered the Garden of Gethsemene until the moment he gave his last breath on the Cross. Finally, we come to the Glorious mysteries.
You see, you have nothing to fear from the rosary. Even the most die-hard Protestant may pick it up and pray it with confidence that there is nothing idolatrous or evil about the Rosary, unless one would claim that scripture is idolatrous or evil.