I have a Z1 Motorsports 25 row (setrab core) with thermostatic plate (mocal) and wrapped stainless lines. I live in Central VA and we have all 4 seasons here but not an extreme of any one. I would say in Chicago I would go with 19 row and def a thermostatic sandwich plate and it still may take a while to get up to temp on your oil and you may need to fab a block off plate for winter to help. That's assuming it your Daily Driver and you don't track your car.
Z1 recommends cores like this and a link to their site is below as well since I highly recommend this kit.
19 Row (13" x 1 1/4" x 5 1/3") -- Recommended for most light street applications or applications in colder climates where less cooling is required.
25 Row (13" x 1 1/4" x 7 1/2") -- Recommended for more intense applications where occasional track use will be seen, also for more moderate climates.
34 Row (13" x 1 1/4" x 10 1/4") -- Recommended for forced induction applications, serious track use, or in high temperature climates where more cooling is required. Our most popular core, even though it is our largest standard offer core it still fits great even with Stillen Gen 3 intakes.
Z1 Motorsports 370Z/G37 Oil Cooler Kit