The Polish-Lithuanian Commonwealth, which I'll abbreviate as PLC, was essentially a union between Poland and Lithuania (which was comprised of the majority of the modern Baltic states plus Poland). I'm not too knowledgeable in the politics of the Austro-Hungarian Empire, but I believe it was pretty similarly governed, only there was much more equality between the Poles and Baltics of the PLC. The PLC was formed in 1596, and originally had it's capitals (two of them) at Krakow and Vilnius, but was moved in 1596 to Warsaw.

The PLC was a powerful country in not only Eastern Europe, but Europe as a whole. The PLC was strong enough to defend against neighboring powers, such as Sweden and Russia, and even managed to capture Moscow, although the PLC only held it for two years.

I had to look to Wikipedia to find out about the politics of the PLC, but it seems that it was considered a constitutional monarchy; however, the Commonwealth was headed by Polish monarchs. Monarchs' power was limited by a large noble class. Monarchs had to pledge to uphold King Henry's Articles. The Articles had some interesting points in them, such as the king being unable to create new taxes/tariffs or declare war/peace without parliamentary approval. The king also was to uphold religious tolerance, and one thing that really stood out to me in the context of this time period, is that the king's children could not inherent the throne - the noble class elected the king. Overall, the PLC had a fairly progressive system for the time period in which it existed.

The PLC fell apart for a number of reasons. For one, political strife brought the PLC close to civil war by the 18th century, leaving it vulnerable to outside forces - notably the Russians. In 1768, the PLC became a protectorate of Russia, and in 1795, it was partitioned among Russia, Prussia, and Austria. The next time an independent Polish state would appear on the map would be in 1918, at the end of World War I.