The Prairie Path is pretty well maintained in my experience - I was riding a touring bike w/ 28mm tires on it last week with no issues whatsoever, and plenty of people ride on 23s or 25s. A used 80's steel road/sport touring bike, something like this: http://chicago.craigslist.org/wcl/bik/3128831153.html should work fine, and easily fit tires up to 32mm/1 x 1 1/4in. Just using that as the first thing that popped up when I searched Chicago CL for "Lombard" (though if you're tall enough to fit that one and it's in good shape, that is a pretty decent deal).

For something less "vintage" I see used Surly Crosschecks and Pacers for sale a lot in Chicago - modern carbon and aluminum road bikes frequently don't have clearance for the tires you need (though some do, especially cyclocross bikes), steel bikes like the Surlys and others from Salsa, Soma and other modern manufacturers (well, branders anyway) will more often have space for 28mm+ tires and fenders (which I'd recommend too, keep that limestone dust out of your bottom bracket).

If you're open to a "vintage" bike, your $6-700 can get you geared up very, very nicely. And the IPP is probably the best maintained limestone path I've ridden on. One thing also, which you've seen is plenty of broken glass - so kevlar-reinforced tires are helpful as well. Good luck!