Excellent answers, as usual. I suppose what I would like to add, as having been received into the Church only a little over a year ago, is to encourage you to also learn the Orthodox understanding of each Psalm as you go. When I began, I reviewed the Psalms for that day using the Orthodox Study Bible and I was amazed how the Orthodox understanding goes far, far beyond the simple moralistic approach I had been taught, even in the more simple explanations offered in the OSB. Christ and the Church begin to literally lift off of the pages. You are in for some great surprises!!
When discussing this with my priest, he told me that it would become a "fifth gospel." I can see now that he was, again, so very correct. At the time, he wrote: "For example, we read: "Blessed is the man that hath not walked in the counsel of the ungodly, nor stood in the way of sinners, nor sat in the seat of the pestilent. But his will is rather in the law of the Lord, and in His law will he meditate day and night." Who is that blessed man, if not our Lord Jesus Christ? What a revelation, if all one had heretofore known was a moralistic interpretation of these words!"
He is sharing with me a copy of St. John Chrysostom's writings on the Psalms and I'm very excited to begin, as I enjoy that type of reading. As others have mentioned, I also use the HTM Psalter and find it most helpful for a "newbie" such as myself.