UU test are commonly used to derive the unconsolidated undrained shear strength of soils. The CU test is used to derive the Mohr-Coulomb failure modes or to generally test soil under undrained in situ consolidation stress conditions. CD test are used for analysing, e.g. the volume change / angle of dilatancy of soil.
Therefore, you should first consider what you want to answer with the triaxial test and then find the test procedure, which is most suitable to answer the question.
There are a variety of studies that analyze the soil behaviour of different materials with regard to UU, CU, and CD test conditions. I can send you papers for a specific soil, but please specify first what material you use in your tests and what your scientific question is.