What contributes to a good egg and healthy embryo?

A few ideas. A good embryo comes from a good, egg, and to a lesser extent, good sperm. Nutrition, stress, alcohol use, smoking have all been shown to contribute to egg quality. The type of stimulation used in ivf has a big effect, and there are medications available that will improve the egg yield in women experiencing problems with stimulation.
Age. Generally, age is the biggest predictor of healthy eggs and embryos, however other factors may also contribute such as pcos, endometriosis, sperm fragmentation, genetics...