Altar Book, p. xx:
"Any psalm can be sung to any tone. It is best, however, that the tone, which can range from cheerful and bright to somber and austere, be appropriate to the text."
My interpretation of this rubric:
More towards cheerful and bright - A-F. I, J
More towards somber and austere - G-H, K
I'd also add that to me the simplest tones are these:
A, D, E, G, H, and I.
P.S. It would have been a great service if LSB had noted which Psalms end up having an even number of divisions, so that the double-Psalm tones could gain wider currency. I have noted where they occur in Treasury; that doesn't help for Introits and such.