I still don't know if the mitochondrion or chloroplast was first? I've looked for it on the internet and in various books but haven't found anything. Does anyone have the answer and a theory which backs up this answer?
Mitochondria evolved before chloroplasts.
We know this because Mitochondria form a monophyletic group: e.g. all life with mitochondria traces back to a single common ancestor (source). Since the group with chloroplasts groups within this clade, it must be the case that either (a) chloroplasts were obtained by an organism that already had mitochondria or (b) chloroplasts were independently lost by multiple lineages within the Eukaryotic clade and then many of these lineages re-acquired chloroplasts by secondary endosymbiosis. Since (a) is a (much) more parsimonious explanation it is the one it makes sense to accept.
According to my knowledge, this was the molecular and cellular evolutionary path of life.
From here you have two main branches, organisms with branched lipids, and with unbranched lipids (the first will become archaea, and the latter urkaryotes and Bacteria)
In the Urkaryotes, you have selection of complexity. Their growths is inefficient, and they tolerate extra DNA. Bacteria favored efficient growth, autotrophy and loss of extra DNA.
At this point the endosymbiosis occurred (presumably), and the bacteria became a very specialized parasite. Mitochondria as you probably know, have their own genome which replicates independently from the nuclear genome. Cells and mitochondria became permanently linked when the mitochondria "decided" to relocate parts of it's genome to the nucleus, incorporating it's genome in the host's.
Now we have the first Eukaryotic organisms that are similar to today's. They were heterotrophic, but one more event of endosymbiosis occurred. That was the formation of chloroplasts.
Many people think that autotrophy is more primitive compared to heterotrophy. That simply isn't true. The conditions when these organisms arose were quite different. Building blocks were readily available and plentiful, so the organisms were all "friends" with each other. It is when food became scarce that selective pressure started nudging species into different directions (autotrophy).
I do not have a definitive answer but I can argue that mitochondria came into existence before chloroplasts despite the fact that, between their free living ancestors- $\alpha$-proteobacterium and Cyanobacteria, the latter seems to be older in evolution.
I have following points to support this argument:
Usually a cell has many mitochondria but fewer chloroplasts. Though this doesn't say much about the evolutionary age but higher number allows more organelle to nuclear gene transfer, considering the limited transfer window hypothesis. More the transfer, more "dependent" will the organelle become on the host.
Even though I claim in the first paragraph that Cyanobacteria is older than $\alpha$-proteobacterium (In fact I dont have a strong reason to support that claim), it doesn't mean that photosynthesis has an older origin. Chemosynthetic pathway and membrane bioenergetics have evolved very early on. Coupling of light to assist these processes, most likely came later when organisms surfaced to the limnetic zone.