Hi Kathryn, and welcome to permies! I admire your willingness to be a steward of a piece of land with a history of abuse, and think that it was lucky to find you.
If you're able to get a soil test done, by all means do so. The things you are probably most concerned are heavy metals like lead, mercury, cadmium and arsenic. Next you might want to know about persistent organic contaminants like used motor oil, diesel, solvents, paints, etc. Then there are the nasties like asbestos, which could be an issue if the place was used as a dump for old building materals.
As far as remediation goes, there are a few things you can try. Mycoremediation with fungus can clean up organics. Bioaccumulators such as sunflowers will take up heavy metals, but then you need to cut them down and take them "away" once they have stored the toxins they took out of the soil. You can also build raised beds with barriers to prevent plants rooting in the contaminated soil if you really want to grow things but are uncomfortable with what they might absorb.
I'd probably go with a staged approach, depending on what the tests came back with. Raised beds and containers to allow you to start growing, and rotations of wood chips with mushroom slurry followed by crops of sunflowers to be carted off to some place that is set up for that sort of thing. After a rotation, get another round of tests on the soil to see what effects you've made and if you're happy with the results, start planting in it and move your remediation efforts to another part of the section