...with thankfulness in your hearts to God. Col. 3:16
And with the LSB, Psalm singing is a cinch! First, LSB got rid of the cumbersome method employed in LW of distinguishing between a three syllable and two syllable ending. Once a person starts psalm singing, it becomes purely intuitive.
LSB does not assign the Psalms printed in the volume with specific tones, but 11 tones are printed in the book and there's no reason one can't use other tones not in the book. Now, understand, the LSB tones are not the beautiful Gregorian tones of the Brotherhood Prayerbook. But they are much easier to master and so quite simple for a congregation and group of school children or a family to learn.
What I would suggest is picking out just two or three tones and thoroughly mastering them. The more solemn tones are E, G and H (LSB p. xxvi). They are very suitable for any Psalm, but especially for those expressive of contrition or distress. Of the more jubilant tones, my favorites are A, D and F. They are great for any of the Psalms that express overflowing joy at the presence and gifts of God.
I have to say that some strike me as clunkers - purely a subjective judgement, I know. I would not waste time on B or C.
The inclusion of two verse tones is a very nice feature. Of those, I think I is the better. Just make sure you have an even number of verses before embarking on one of those. And since they are a little trickier, I'd be inclined to leave the two verse tones (I, J, K) aside until having mastered a number of the single verse tones.
It's a great joy to sing Psalms to the Lord, and with LSB that great joy is simple to learn.