As you're discovering, taxing formulas are rather complicated and involve assessed values(which fluctuate) of both land and the building, % of lot improved, multipliers, etc. It's not just the square footage of the house that's taken into consideration, but also the size of the lot. Generally, however, you would expect to pay at least $13,000in taxes for a 3500-3600 square foot house in Lake Forest. Upgrades and location are also factors that can impact taxes. There aren't many single family homes in the Lincolnshire/Vernon Hills area with only 1600 square feet. However, you could expect to pay in the $6000 range.
I'd be glad to email you a sampling of listings for you to review to get a better idea of what's available in those home size/tax ranges.