Like most of the old NW, Wisconsin was explored early on by the French. Green Bay was established as an outpost in 1634, a Jesuit mission site in 1671 and a fort was constructed in 1717. Other settlements and fur storage outposts were established during the 1600s into the mid-1700s.
The British gained control of Green Bay in 1761 and had full control of the territory by the end of the French and Indian War. Early on, the British, like the French, were primarily interested in the fur trade.
The US gained the territory in 1783, with Massachusetts and Virginia claiming the region. It became part of the NW Territory in 1787 and the Indiana Territory in 1800.
Prairie du Chien saw the only major action during the War of 1812, with the British capturing Fort Shelby in July of 1814, which had been built by the Americans.
The Winnebago War  and Black Hawk War  marked the major conflicts between the US and Wisconsin's natives.
Lead mining spurred the growth of the territory during the 1820s and 30s. Mineral Point, Platteville, Shullsburg, Belmont, and New Diggings sprang up was boom towns around the mines. Those towns were followed by the settlement of Milwaukee.
Wisconsin became a territory in 1836. Belmont became the first capital, but deemed too small. Madison was then built to become the first capital, with Burlington [later part of Iowa Territory] serving as capital in 1837. Wisconsin became the 30th state in 1848.
Family connections: The McHugh family moved to Wisconsin from Illinois in 1848. The Wagner/Laubscher clan also arrived from Missouri that year. Both were drawn by the lead mines. The McHugh were also attracted by the opportunities for masonry work.
WI Reading: https://en.wikipedia.org/wiki/History_of_Wisconsin