Not a bad question at all!
I concur with the telephone methods mentioned earlier. But if the weather is low you might have a problem.
Any CFII’s, please feel free to correct me on this (I am IFR, but not CFII, so don’t take my word as gospel), but you have to maintain VFR until you can enter controlled airspace (class E), which looks to be 700 ft AGL in that area. If there is overcast below that, you can’t fly in it while in class G airspace.
KPWK and KDPA are both class D and controlled airspace goes all the way to the surface, if you have a choice.
If the weather is good VMC, I might consider departing VFR and picking up the clearance via radio AFTER clear of the Chicago area due to the freq congestion. But on the other hand, lots of radio traffic means lots of airplane traffic, so if any doubt at all, go the telephone route. Even though VMC, ATC will give you an initial vector that will keep you out of the way of the major airport traffic until they get you on radar.