I've configured the Shared Documents Library on an out-of-the-box Team Site to use the custom Content Type Legal Contract as the default Content Type of the Library. If not sure how to do this there is a blog post that steps you through the process: Create a Custom Content Type In SharePoint 2010
 

I start by adding a Contract using the New Icon button in the ribbon and selecting the Legal Contract Content Type (the only choice because of how I set up the library)

I fill out the contents of the Document Information Panel (DIP) and hit save.

I name the contract with the contract number and save it back to the Document Library.

I adjusted the default view to show the Site Columns and Content Type. Notice the Add Document Button?  I want to get rid of this so users will only have the choice of using the New Button in the ribbon.

I go to Site Actions> Edit Page. Since this is a web part page, I will edit the properties of the Web Part to hide the Add Document button.

I use the drop down arrow of the Shared Documents Web part and choose Edit Web Part.

Using the drop down list of the Toolbar Type, I change the selection from Full Toolbar to No Toolbar and click OK

I notice that the Add Document Button is now gone. I navigate away from the page and back to refresh the page to make sure the change took effect.

Now I can clearly see the Add Document is missing, success! Now I'm going to update the Home Page.

I navigate to the Home Page of the site, which also features a Web Part to interact with the Shared Documents Document Library and there's that old pesky Add Document button.

I click on the black ufo triangle to get to the Edit Web Part choice and click it (I just call it the black ufo triangle…don't ask why)

I make sure the Selected View says "All Documents" and then change the drop down menu for Toolbar type to say No Toolbar, as pictured above, then click OK.

Voilà, the Add Document button is gone!  That's how easy it is.