The Psalms have been called the prayer book of the Church and a nice little introduction to them is Reflections on the Psalms by C. S. Lewis, which I read a month or so ago. Lewis does a good job of talking to the reader about things in the Psalms that might seem odd to modern Gentiles--cursings and anger (in a holy work?!) or the idea of God's law being sweet.
The most notable chapter, to my mind, was the chapter on praising. Lewis said that when he was on the cusp of Christianity the repeated exhortations of some Christians to praise God was one of the more hard to understand things for him. Why praise? Why would an omnipotent being care if he were praised or not? After a couple of brief bits on this, he shares the realization that came to him: that the everyday world is full of praise and that, in a sense, our enjoyment is not complete until we praise. When we see a movie we love, what do we do as soon as it's over? We turn to the people we saw it with and say, "That was great! Didn't you love that part where X happened?" If we talk to a friend or coworker who hasn't seen it, we say, "It was great, you have to go see it." If we have a good meal, it almost isn't complete until we express our enjoyment verbally. Most of us love the chance to praise a family member, even if it's only to outsiders and not to the person himself. And people who are healthy in mind and spirit are even more apt to praise than others; they will not stint their praise of something good in parts because it was not perfect in all.
But Lewis says all of this better than I do. Check it out. I found this book at my public library, but it's available inexpensively at Amazon in a paperback with a pretty cover, as well as in an audiobook download. I would recommend this book as a gift for nearly anyone. Being composed of short, more or less stand-alone type chapters, I should think it would suit people who don't read much, and it might be a good corrective to anyone who, never having read much of it, assume the Bible is full of Precious Moments moments.