When I joined the Episcopal Church in the spring of 2012, they gifted me a small, soft-back copy of the Book of Common Prayer. The BCP has some really lovely prayers in it and includes the Psalter as well.
A friend of mine who's also a former Episcopalian has long recommended the use of praying through the Psalms to deal with various emotional conflicts as the Psalms take us on such an essential journey.
The mystical perspective of praying the Psalms has to do with each Psalm containing a Name of God in Hebrew, and that by praying the Psalms, one activates the power of those Names. (This is related to the practice of Seed Thought meditations that we seminarians go through.)
In the traditional praying of the Liturgy of the Hours, various Psalms are prayed on the daily. I've heard that the practice of praying the Holy Rosary emerged from monks praying through all the Psalms daily at one point in history, but I'm unsure of how accurate this is and would have to research it.
Either way, I encourage everyone to pray the Psalms; offer the prayers to God on behalf of someone who needs that good energy.