I'm located in the Chicago burbs too, so here's my experience with hops:
1. I've been very happy with the rhizomes I've purchased from Arrowhead Hops arrowheadhops.com. They're in Iowa, so the rhizomes you're getting are from plants that were grown in a climate more similar to Illinois. The rhizomes I've planted from them have done really well in the first year. I'm making an educated guess that it's because of the climate similarity. I've also purchased some from Hops Direct hopsdirect.com that have fared well.
2. Never tried plants, but hops are pretty hardy, so rhizomes have always been fine for me. I've only had one fail to grow out of probably about a dozen.
3. I'd say the second option is better. They want to grow up as much as possible, so let them.
A final bit of advice... Have a plan to combat Japanese beetles. They seem to have a preference for certain varieties (Willamette and Centennial in my garden). They only want to eat the leaves, but I'm sure it slows the plants' growth down. I just spray with water daily to knock them off.
Not sure where in the burbs you're located, but if you need any rhizomes, I can cut plenty off my plants and give them to you. My Goldings and Willamette have huge root systems, so I could cut lots from those. My Chinook may be ready for some cutting too. PM me if you're interested.
Thanks for the reminder, I lived in Iowa last year and remember asking around out of curiosity and heard that same name. And as for the Willamette rhizome, I might have to take you up on that offer, I will let you know when it gets a little closer to spring.
And thank you everyone else for the advice, learning new stuff everyday. Now I am really looking forward to this summer, regardless of hop growage.