This is a great question because it’s really more about thinking things through than getting a definitive answer.

You are correct that the first organisms were heterotrophs. They got their energy from breaking down large organic molecules. We don’t know what they were “eating.” Was it hydrogen sulfide like the creatures that live around hydrothermal vents at the bottom of the ocean? Maybe. We know they didn’t have mitochondria, but one type apparently became mitochondria sometime after eukaryotes evolved.

At the level of the individual, one can obviously live without chloroplasts. If you look at a tree, you can see that only a tiny fraction of its cells have chloroplasts. The cells in roots, trunk, and branches, even some of the cells in the leaves, don’t have chloroplasts. But all those cells have mitochondria for breaking down the sugar made in chloroplasts.

You and I don’t have chloroplasts and do just fine. But what about on the ecosystem level?

We wouldn’t last long without plants to make our food (or our food’s food) and pump out oxygen for us to breathe. I suppose we could get by if enough prokaryotic producers (cyanobacteria) were around. But the world would be entirely different without plants to stabilize soil, cool the earth by shading and transpiration, produce wood, and provide habitat. Earth might be able to support Eukaryotic heterotrophs, but things would be pretty bleak for most animals.

Would you want to live in a world with no plants? Do you think a world with no eukaryotic producers would support as much biomass as Earth currently has?

It’s hard to say which is more important to life on Earth because both are critical for survival. Without chloroplasts, plants would not be able to get their energy from the sun and would cease to survive, leaving us without food. On the other hand, without mitochondria, animals would be lacking in cellular energy and would also fail to survive. Therefore, both are critical to our survival on Earth, and missing either would be detrimental to our survival.

The first organisms may have been autotrophs, but they didn't rely on photosynthesis. They relied on chemosynthesis instead, by exploiting chemical gradients in volcanic vents, etc. Also, chloroplasts and mitochondria are found only in eukaryotic cells; bacteria and archaea do not have them. Indeed, both chloroplasts and mitochondria are descended from once free-living bacteria! The still free-living relatives of chloroplasts and mitochondria do similar things in their ecosystems that chloroplasts and mitochondria themselves do in cells: cyanobacteria photosynthesize, and aerobic heterotrophic bacteria oxidize sugars. Since oxygen is poisonous in too great quantities to both, but also necessary, the two processes are about equally important.

The chloroplast, because it makes food for the rest of us animals and fungi and such. Bacteria and Archaea don't have mitochondria, and they do just fine. Cells can break down glucose part way without mitochondria. The mitochondria break down the 'pieces' of glucose into water, carbon dioxide, and chemical energy.