Remember that the Psalms are very important. They are not simply prayers - they are the experience of God that Israel made (and still makes today, the Church being Israel), not through history or through prophecy but through praise of God.
IMO it's good to read 5 in the morning and 5 in the evening. It's a fine pace, beside Psalm 119 being a nightmare. You could even say it replaces your morning and evening prayers.
There's a lot to meditate on (regarding how these prayers and songs express a truth that is both lived in our Christian life, and fulfilled in the gospels), and also, notice that the Psalms are divided into 5 parts:
- Book 1 is Psalms 1 to 41
- Book 2 is Psalms 42 to 72
- Book 3 is Psalms 73 to 89
- Book 4 is Psalms 90 to 106
- Book 5 is Psalms 107 to 150
I have noticed that the Psalms are divided in such a way because they tell a story. But this story is not told explicitly, but rather through independant "patches" of prayers, so to speak. Sort of like drawing a picture by cutting and pasting parts of other pictures together.
I find that the theme of Book 1 is "The righteous man oppressed by his enemies". The theme of Book 2 is "God's universal judgement". Book 3 is "God and Israel". Book 4 is "Awe for the glory of God, and repentance". Book 5 is "Explosion of praise for God".
One could very well meditate on how these 5 books, with their themes, relate to the 5 books of the Law, and to the 5 distinct parts of the gospel of Matthew (designed to reflect the Law) as well.
This is just an example for the sake of Bible study. It's up to you to meditate on those texts and find the bread of God underlying within. But don't skip the Psalter - it's one of the most important books of the Bible.
Don't skip Proverbs either.