So, here's the best advice I can give from personal experience. I've long suspected that the point of the Holy Rosary, in its repetitiveness, which is held in great disdain by the Modernists, was to ANCHOR part of the mind on the repetitive "automatic" recitation of the words, so that once that part of the mind is anchored in, the other part of the mind is free to drift up to meditation and potentially even contemplation. Even some of the Eastern religions employ this same technique.
Psychologists have done much study on how certain repetitive actions end up being just filed away in a certain part of the brain where you just start doing them without being consciously aware of them, and that's so the rest of your mind can be freed up to do other things. Take, for example, a familiar commute in a car, say to work or school or to some place you're used to going. You don't actually sit there and consciously think through it ... "Now, turn right up ahead, and then go a couple miles, and turn left at that light." You just do it and do not need to engage your conscious mind, since your brain has tucked it away somewhere to free up your other faculties for other, more useful thinking.
So, the point of the Holy Rosary is PRIMARILY the medication. Now, unlike with the Eastern religion, we fill the automatic part of the brain with actual Catholic thoughts, the words of the Hail Mary, whereas the danger with the Eastern forms of "non-thinking", where you empty out the mind with non-sensical chanting of sounds, is that various other non-Catholic things and even entities can find their way in there. This kindof forces those things out.
That is why Our Lady asked specifically for 15 minutes of meditation on the Mysteries of the Holy Rosary for the Five First Saturdays, because she noticed that many people just rifled through Rosaries by saying the words, and it was not having the intended effect of encouraging them to meditate.
After all that, by far the most fruitful practice I have found for praying the Rosary is to actually pause between each decade and spend a good 5 miniutes, at least, possibly longer if you have the time, meditating upon the actual mystery of the decade to follow, and only THEN beginning the Our Father and the Haily Marys. St. Therese at one point felt guilty about not liking the Holy Rosary, but she was referring to where they were reciting it together in common (which has different benefits, serving as a profession of faith), but she mentioned how she could spent a long time just thinking about each phrase in the Our Father. In other words, she was already inclined toward meditation and contemplative prayer, and so just running through the words didn't do much for her. But I'm sure if she were praying alone and could take her time, then it would have been magnificently fruitful for her.
That's one reason, for instance, that I cannot stand saying the Rosary while driving, since I get the feeling that the Rosary and my focus on driving are competing with one another for that same part of my automatic brain.