There are a couple of ways you could set up your desired workflow however please note that you will not be able to do all of this with just one link. You'll either need to generate a unique URL for each recipient, or you can use email to initiate the requests. Both are very easy to setup.
In the DocuSign system there are two general methods for initiating your signature requests-
1. Email Delivery
2. Embedding Feature
I'll briefly describe each but for a good explanation of the differences please see this page from the DocuSign Developer Center
http://www.docusign.com/developer-center/explore/features/embedding-docusign
When you setup signature requests through the DocuSign Console they are sent using the first method- Email - and the recipients are known as "remote" recipients. This means that each recipient receives an email when it's their turn to sign, and they start the signing workflow by clicking the link in the email request.
You can add as many recipients you want to the envelope and using the Routing Order property you can control the order that each recipient signs the documents. If two recipients have routing order 1 and 2, for example, then the second recipient can not sign until the first recipient is done signing. If they have the same routing order, then they can sign at the same time.
With the second method - Embedding - your recipients are known as "captive" or "embedded" recipients, and they will start the signing process directly by clicking on a hyperlink (i.e. instead of waiting for an email and clicking from there they can access it immediately). This is done by generating a URL token. For more info on how to create URL tokens for your recipients please see the above link to Dev Center.
You can intermix your recipients on a given envelope, meaning you can have embedded and remote recipients in the same envelope, so if you want you could make your Procurement Manager an embedded recipient (so that they start signing by opening a URL) and then all the remaining recipients remote recipients so that once the procurement manager signs the system then automatically emails the next manager for their signature, and so on. Or if you don't want to ever wait for any emails then you could make each recipient an embedded one, but they will still have to at least click a link (or have one automatically opened for them) to start their signing workflow.
The two best resources for this are the above link, which I'm referencing here again, and the API Walkthroughs. The last three walkthroughs all focus on Embedding DocuSign...
DocuSign Embedding Feature
DocuSign API Walkthroughs