Does it matter what herbicides I use on my crops before planting prairie strips?
Yes, the herbicides you use on your crops matter, especially when you are trying to establish prairie strips. Many alternatives to glyphosate will last in the soil for more than one season. There are planting restriction guidelines provided by manufacturers and you can refer to these to find out how long a herbicide will last and what crops are sensitive to it. (Prairie seedlings aren't listed separately, but would respond much like small grains, alfalfa, and clovers.)
The Crop Data Management Systems, Inc. website provides a database of herbicide labels that can be searched using either the common name of the herbicide or the product manufacturer. Follow the links at the top of the page for ‘Label Database’ and then search via product name or manufacturer.
You also can compare different herbicides using a table from the 2015 Weed Control Guide for Ohio, Indiana and Illinois. View or download their “Restrictions on Crop Rotation” table here [PDF].