Heterotrophic cells presumably evolved first, followed later by those species capable of photosynthesis. It is interesting that your question asks about "plant cells" and "animal cells" as this implies a level of multicellularity and specialization, which these earliest forms of life did not exhibit. While not animals in the traditional sense (not being heterotrophic multicellular organisms), there are unicellular species that are both motile and photosynthetic. Good examples would include members of the phytomastigophorea which contains species such as the common freshwater Euglena.

It is also important that when thinking about evolutionary processes that you avoid looking at things from a teleological perspective (the use of design or purpose as an explanation of natural phenomena). Species don't "decide" to evolve in one way or another, but rather, those species with unfavorable or inferior characteristics are simply out-competed and subsequently, their genes do not make it into successive generations.

Most species of animals have such high surface area to volume ratios and high activity levels, that relying on photosynthesis would probably contribute negligibly to their metabolic requirements. There are however, some exceptions, but for photosynthesis, these species rely on algal endosymbionts (frequently dinoflagellates) to provide supplemental nutrition. The contribution of the endosymbionts to the host's metabolic needs can vary dramatically from species to species, from very little to 90+%. It should be noted that the appearance of mutualistic algal-invertebrate symbioses evolved independently in a wide range of taxa and includes a large number of species including sponges, hydroids, jellyfish, anemones, corals, sea slugs, bivalves, and flatworms, among others.