I used to ride the prairie path from St. Charles to Naperville several times a week. It's funny that my most commonly used route for the commute was almost exactly 34 miles too. I did it on a variety of bikes such as a fixed gear with no tires ever wider than 25mm, a single speed cyclocross bike with 32mm tires, and an old rigid mtb with 2" touring tires. All of them did fine when it was dry and honestly all of them were close enough in speed that it really didn't make much difference which bike I was on. Maybe that is because I have almost always used a rack and panniers.

If you get caught in or after a heavy rain though or during a time of thaw in winter or spring, the wider tires of the mtb are the way to go. The narrower tires just cut through that packed limestone like a hot knife through butter when the trail gets wet and soft. IMO fenders are an absolute must for regular commuting on something like the prairie path. The bike, drive train, you, and your gear just stays so much cleaner with fenders, especially when you factor moisture in. If I got caught on a bike without fenders on the trail when it was raining heavily, I would usually have to hose myself down before going into the garage when I got home.

If I was still doing that commute and had to pick one bike to do it with, I would probably go with another single speed cyclocross or touring style road bike that could take at least 38mm tires with fenders. I would seriously consider a IGH if I though I needed multiple gears. Keeping the drive train clean is so much easier that way. Even if you avoid most of the white muck by not riding the trail when it is wet, the dust is still a pain in the rear during dry conditions.

Something like this might do, but they always seem to sell out of them before I decide I want one enough to pull the trigger.

http://bikesdirect.com/products/mercier/kilott_wt5.htm