There's a bit of a controversy over Koguryo. If you visit some Chinese sites (such as the "People's Daily"), you'd notice that they refer to Koguryo as a part of
Chinese culture. As I've mentioned before, Chinese have a very bad habit of claiming everyone.

Parhae ("Bohai" in Chinese), which formed from the remnants of Koguryo and absorbed much of Jilin and parts of Heilongjiang region, was founded by a Koguryo leader (Dae Jo-young, who I mentioned in the other thread). However, Chinese claim that Dae Jo-young was not Korean, but Malgal ("Mohe" in Chinese). This is perhaps due to an attempt on the part of the Chinese to distance Parhae from Korea.
A theory positing Japan as a colony of Paekche is one that I've never heard of before. It's an intereting theory, but I kind of doubt it.
The nice thing about Asian history is that there is so much quirky controversy over minor details.
Of the three kingdoms, Koguryo started out as the strongest and most advanced. Shilla was largely tribal. It became a major power in the region when it sided with China. Politics regarding each of the kingdoms' stance towards China played a big role in the balance of power in the region.

Their technology should be comparable to that of China at the time so you could base some of the tech tree on Chinese technology of that period.