If your local university doesn’t test for the specific contaminants you’re concerned about you can send samples to a private lab instead, sometimes they offer more testing options. I don’t know the specifics of how each one is tested for, but on your end they usually just require you to take (and possibly dry) soil samples before sending them in.

If you don’t have a good idea of the history of the site, it would be good to try and figure it out through your local historical society if you have one, or land records from your local records office. Whoever is testing the soil will have a better idea of what to test for if they know it used to be a mining town, or it’s 50 feet from a house old enough to have used lead paint, if it was farm land, etc.