I think that this article might be helpful:
“Exotic Preferences for Macroeconomists”
They give a thorough explanation of many preference functionals and show their usefulness with macroeconomic applications.
Im not a specialist in macroeconomics, so I dont know the literature that well, but I think that the most used preferences nowadays are the Epstein-Zin preferences. The article I cite discusses thoroughly their properties.
A nice thing this paper has is that it contains detailed comments from Peter Lars Hansen and Ivan Werning among others at the back.
Hope it helps!