What type of climbing rose grows well in a Northern Illinois climate?

Depends on your gardening zone. The colder your area is the fewer the choices are. If your zone is in the colder part of zone 5 and below your best choices are Canadian bred 'own root' roses. These are more likely to be available at rose plant retail sites on line. Do a google or yahoo search for 'Climing Rose Plants for cold climates' or 'own root rose plants'. You can also check info at your county's Cooperative Extension site for recommendations for roses that do well in your area. Best bet for climbing roses is to choose one that is hardy to at least one zone below yours. This will give you a better chance to avoid winter 'cane damage'.