Here in Illinois, and likewise in the Midwest, professional foresters usually recommend a 10 x 10 or 8 x 10 spacing for newly planted hardwood trees (i.e., 10 x 10 spacing is equivalent to planting trees on a grid/contour 10' between rows and 10' within rows).
10 x 10 = 436 trees/acre
8 x 10 spacing = 545 trees/acre
Another factor to consider is the cost of the seedling stock and whether or not you are receiving any cost-share assistance from a state or federal agency as part of your conservation tree planting efforts. Another factor to consider is the planting site and the prospects of planting failure: poor planting sites (i.e., shallow, dry, low fertility soils) or sites that are subject to frequent flooding may require higher densities (e.g., 8 x 10) to achieve your desired objectives.
Again, here in Illinois we generally plant hardwood trees on 10 x 10 or 8 x 10 spacing.
Best of luck!