I was always taught in my schooling that it was the Mongol Empire that first unified China; but I've always had a problem with that. Now, they were the first group to conquer all of what is now apart of China, and the only other dynasty to do that was the Qing who came after (interesting how the two times China was at its largest was under the control on non Chinese).
But would you consider everyone in China as ethnically Chinese? To pit it VERY plainly and simply, you have groups such as the Manchurians, Mongolians, Koreans, Tibetans, the people of the Xinjiang area, and S.E. Asians like the Vietnamese and Myanmarese.
Wouldn't it make more sense to say China as in the Chinese were first unified by the Qin, the third main dynasty and first Chinese Empire? (That is if you go with Xia and Zhao being main Dynasties and Shang wasn't)
Here is a picture of the [Qin Dynasty] (http://i.imgur.com/QeRVWyt.png). That area is ethnically Chinese, wouldn't that make more sense for when China was unified and everything else was extra territory gained? Sure the [Mongol Empire] (http://i.imgur.com/KGbtaqg.jpg) controlled so much, and the [Yuan Dynasty] (http://i.imgur.com/uo2M56k.png) right after it and [Qing Dynasty] (http://i.imgur.com/sKrIOIK.png) a few hundred years later owned practically all of modern China. But honestly that's something that's always bothered me about China's unification.
To hold the Yuan Dynasty/Mongol Empire as the unifying power of China is quite strange. May I inquire as to where you are from?
But first, to answer your question! Your question is somewhat odd by itself - why does China need 'true unification' anyway? Chinese civilization has existed since 1600 BC (Shang Dynasty), and it has slowly grown over time since then. If you mean "When was China first unified?", then it would have to be asked in conjunction with "When was China first fragmented?"
If those are your questions, then China was first fragmented during the Warring States period, and after that it was unified by Qin Shi Huang, who ushered in the Qin Dynasty and China's first instance of imperial dynastic rule.
Qin Shi Huang accomplished many great feats as the first real Emperor of China, unifying the fractious Warring States, establishing a unified language system, and a highly structured political and military framework. He pursued legalism and a system of direct administrative power stemming from the imperial court, which curtailed the power of the feudal aristocracy (who contributed greatly to the erosion of Zhou power).
He was also, however, a tyrannical dictator, whose empire did not survive his death. However, since the succeeding Han Dynasty effectively adopted many of his political and social reforms, and was much longer-lived and held in much greater regard, the Chinese like to regard the Han Dynasty as the first "true" dynasty of China.
In spite of that, the Qin Dynasty is undoubtedly the first imperial dynasty, tyrannical or not.
Your question also seems to be asking something along the lines of "When were the various ethnicities and minorities within modern China unified?"
Well, those various minorities didn't really "belong" to China, per se. Rather, they were assimilated into China either because of Chinese conquests, or the opposite: because they were conquering powers who took over China and became sinicized (Mongols, Khitans, Manchurians, etc). Over time, they became accepted as Chinese peoples, alongside the majority Han people. Different minorities became part of China at different times, so this is hard to answer without basically telling you "the Qing Dynasty!".
If you want to clarify some of your questions, I can provide more insight where needed.
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