Reading the Psalms is one of the devotional practices I recommend over and over again. The question I often get in respond to my recommendation is which translation to use? My standard response is use the one you are familiar with already. By using a translation you are familiar with whether based on the Septuagint or the Hebrew text, it is already in your memory and much easier to make the Psalms your prayer.
I grew up a Lutheran using TLH so the Coverdale Psalter is the translation of the Psalms I am most familiar with. So when I pray privately the Psalms that is what I use. This is the same translation that is used in the 1662 Book of Common Prayer.
The only restriction I put on the above recommendation is do not use an inclusive language translation. The main reason I avoid inclusive language translations is the Christological nature of the Psalms are lost. The Psalms are the prayers of Jesus. When Jesus cries out on the cross,"My God, my God, why have you forsaken me?" He is praying the Psalms. When Psalm one says,"BLESSED is the man that hath not walked in the counsel of the ungodly, nor stood in the way of sinners." this is a reference to Christ not us sinners. Inclusive translations usually translate the singular male noun or pronoun as a inclusive pronoun. For example, the Inclusive translation of the Grail Psalter starts with," Happy are those..." The translation completely destroys the Christological nature of the Psalm.
What if you are new to praying the Psalms, what translation should you use? The short answer is use the one your parish uses. My parish uses the Psalter for Prayer. This translation is an adaptation of Coverdle's translation to match the Septuagint text. So if you were in my parish that is the one I would recommend. Check with your priest which is one the parish uses. There are several good Septuagint based Psalters, Psalter for Prayer, The Psalter according to the Seventy, the Ancient Faith Psalter, and the Psalms in the Orthodox Study Bible. So most likely they are using one of the above.
Some of you may have noticed I am pointing out translations based on the Septuagint but personally I am using one based on the Hebrew text. There are differences between some of the Psalm texts which are important to know for study and liturgical use. Private prayer and devotion are another matter. Using words you are familiar with in prayer are more important than whether they are based on a certain translation assuming the translation is not problematic in someway.Also please note my use of a Hebrew based translation is for private devotion not liturgical use. I do use a Septuagint based translation for liturgical services.