You're already on the right track trying to devise a plan and seeking help to do so. The suggestions above, including the photo requests sound like reasonable ideas. I know that when I have a project/situation that I see to be a bit overwhelming, I try to compartmentalize the issues and goals, and then try to resolve it in stages. This way, the enormity of the project/situation is not weighing on me so much. You also need to define you expectations. Are they just removing the junk and making a reasonable yard/lawn, or are you looking to plant an elaborate landscape with finely manicured lawn. You need to set reasonable goals and timelines for your expectations. That being said, I have a few suggestions:
1. Plan short, medium, and long term goals. I'm sure that you want it to be resolved ASAP, which means different things to everyone. To some, it literally means tomorrow. To others, it may mean a growing season or two. You need to determine what your timeline is, before you proceed. Then you can determine how long you want your short, medium and long term goals to be. Obviously, cost/budget is a major factor, so I'm mentioning it here.
2. Once you figure out #1, we can help get you where you need/want to be in a reasonable time period.
3. Since you mention the yard is a big mess, it probably couldn't get too much worse during the construction. However, I would suggest planning so you don't make things look worse in the interim, in case you get held up on the next step. What comes to mind is the large debris in the brush. If it's going to take awhile to remove the car parts and dish, don't cut away all the brush, so it's visible and even more of an eyesore from the house. If it's so badly buried that you need to cut it out, to get it out of there, try working from the rear, and remove the metal in stages. If the metal is too large for you to handle, consider renting or buying a plasma cutter (and generator, if necessary). Just make sure you have a hose, fire extinguisher, etc. ready.
4. Depending on your budget, consider renting a skid steer, if you want to accomplish things quickly. You may be able to knock out a lot of work quickly. Especially, if you get more than one attachment delivered with it. If this is an option, we can guide you on which attachments to rent. If you are on a shoestring budget, chipping away using smaller rental equipment may be the way to go. Running a rolling magnet in conjunction with a rototiller may be something to consider, once you get all of the big metal pieces out of there. It will help, but you will always have debris surfacing, unless you cut out the soil and replace. It seems to always work its way to the surface. Unfortunately, I know this first hand from my own backyard. I just tolerant it and pick up the glass and other debris as it surfaces.
5. Write everything down on paper to help brainstorm and break things into categories during the planning stage, and as idea comes up along the way. You can jot notes or ideas quickly, and always type it up later, if you are records obsessed. I found it helpful to put pencil to paper for projects like building my deck. Also, track progress with photos.
6. Speaking of photo. May we have some, please?
I hope this helps.