1. What kind of car parts and plastics? What kind of volume of materials? Garbage was/is often thrown into construction. You'd be amazed at what gets pulled up from this kind of work. Also, there is a possibility of asbestos! Make sure you are familiar with what that looks like.
2. What is your budget?
3. Got pictures?

I would avoid planting edibles like the other poster suggested until you know exactly what you are dealing with and what plants interact with what. There are cheap soil test kits about as well. Brassicas, for instance, one of the largest families of cultivars (if not the largest), love sucking up LEAD.

I hope, too, you use PPE when doing this work. I know in commercial archaeology, we are required to really cover our asses with it when working on contaminated sites. See here.

Also, these may be of use:

• Clean-Up of Heavy Metals from Contaminated Soil by Phytoremediation: A Multidisciplinary and Eco-Friendly Approach.
• Chapter 15 - Phytoextraction: The Use of Plants to Remove Heavy Metals from Soil (a while journal of the subject, too!): More than 450–500 plant species have been identified as hyperaccumulators including Thalaspi and Arabidopsis and members from families such as Brassicaceae (cultivars like broccoli), Cyperaceae (sedges), Poaceae (grass), Fabaceae (legumes[!]), and several others
• Wiki list of hyperaccumulators - note the second and third linked tables for other metals listed directly above the chart.
• Cornell Guide to Soil Testing

(Check Anna's Archive if you cannot access them.)

Keywords to search:

• Phytostabilization
• Bioremediation

There are a number of plant databases on the sidebar of !plantid@mander.xyz and !houseplants@mander.xyz that may help. I have to update that list, I think, as I collect them. You may want to check out: U Michigan Native Plants by Region

I was going to suggest prairie grasses, however, their deep roots may or may not be picking up those nutrients and may be more of a defence against wildfires apparently. They may be good, however, if you want something with resilience.

Regretfully, I'd say you're limited to raised beds. You simply don't know what's down there, and how extensive the likely contamination is. You can test for contaminants, but it's going to be pricey. Here's a list of parameters you'd need to test for and their guideline concentrations.

Metals and hydrocarbon testing can run between $50 to $200 per sample. you'd need to sample multiple intervals (depths) and locations to accurately delineate the contamination, or confirm the area for your proposed garden is safe. Not only is there the risk of the buried contaminants, but older (pre-1980s) urban areas are notorious for lead contamination.

Raised beds are great, because they offer you a good deal of control over your growth media. If you really know what you're doing you can create a media that's freely draining and not limited to your site's soil texture, and have a large pool of multi-fractioned organic matter to support your plants. Lots of permacultureists (though i don't like those people) use raised beds to pretty good effect. On top of all that, they're modular. Here is an example cross section, though they've heaped it

The phyotoremdiation thing is feasible, but it's usually just tied to one or two metal types, takes a while, and you have to dispose of the now-contaminated biomass.

You probably want to do a soil test. Depending on what is in there, dust may be the bigger risk. As the other commenter said, you probably don't need to worry about eating food grown in contaminated soil as long as you wash it thoroughly before eating. However, spending a lot of time working out there- breathing in particulates, getting dirt in your eyes, under your nails, and in all the little cuts one gets while working in a garden-could introduce something to your system you don't want.

Good news! Edible plants pull very little heavy metals from the soil (or so I've read). Here's a good article I've found that goes over a lot of your concerns - https://extension.oregonstate.edu/gardening/soil-compost/should-i-worry-about-heavy-metals-my-garden-soil

I've always heard that sunflowers pull bad stuff from the ground. I'm not sure how true that is.