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Having used it a little, Robert Alter's The Book of Psalms: A Translation with Commentary looks to be a highly worthwhile book to have.

Robert Alter has done lots of work over the years on understanding how Hebrew poetry works. Here, he offers his own translation of the Psalms, together with a short commentary on the text. The comments are brief, but insightful. The translation is fresh, and where he differs significantly from most English versions he explains why he translates as he does.

Let me give an example, from Psalm 1:2

Translation:

But the LORD's teaching is his desire, and His teaching he murmurs day and night

Comment:

2. murmurs. The verb hagah means to make a low muttering sound, which is what one does with a text in a culture where there is no silent reading. By extension, predominantly in post-biblical Hebrew, it has the sense of “to meditate.”