"Is there a way to enter a project contract amount"
You will be using your two-side Items, and you will make an Estimate for the Customer, or Customer and Job. Put the Scope here. Put the Price here. Your two sided items should already have a project cost to you on their left side - the Cost side. Now you will be able to run Est vs Actuals reporting.
"and enter sub contracts, purchase orders"
Yes, you are ready to use the same Items for Subs, on the PO. example: You are a Remodeling contractor, so you propose the Scope of work for my Kitchen Addition/remodel as $15,000 Engineering, $5,000 Electrician, 15 Cabinets, $3,500 flooring allowance, etc. These goods and services Items, then, are what you will list on a PO, for those things you need to track.
You might not need to track the Appliances; you will simply go pick up what I show for at Home Depot.
For the Engineering, swap Qty and Rate. That contract is 15,000 Each at $1. Now you can manage Partial Payment requests and see if they Overbill you.
"and other cost against the project amount?"
When you enter Spending details, using Write Check (paper or paperless or debit card) and Enter Credit card charge, and Enter Bill to pay later, you list the Items and Job Track that it is for me, as Customer. You also need to note if that is Billable, under a Time & Expenses contract. Or, Not Billable, because we negotiated a Fixed contract price.
You may think I am following you around trying to bother you, but you seriously have all the answers I need.
So, can you explain a little more about,
"For the Engineering, swap Qty and Rate. That contract is 15(k)....Now you can manage Partial Payment requests and see if they overbill you"
Partial payment requests from a vendor? What side of the equation are we talking about?
Also, I am trying desperately to correct some poor accounting practices here. The "items" options in QBs is the answer. I downloaded and printed your "Quickbooks Accounts and Items Relationships" image.
Can you explain more about using Payments as an item? I don't fully grasp it. Something tells me once I do, I will be able to process Joint Checks much easier.