Sneakers are adequate, but any hard-sole shoe or boot is sure to cause an injury. Note that your shoes will get very muddy. Given the choice between wearing expensive hiking boots or sneakers, I would wear the sneakers on my first trip. Wear wool socks for warmth. Rugged long-sleeve clothing should be worn.
Coveralls are nice.
Your outer layer will get very dirty and might get ripped up, so don't wear anything good. Wisconsin caves are 45 to 50 degrees. People have died from hypothermia at warmer temperatures. Dress warmly, but don't restrict circulation or movement. Wool and synthetics are best because they insulate even when wet.