A field that's a reference to another node that has a reference to another node

Well it's been a week and now I'm having fun with Drupal, but here's the problem.

A project has a contact, and a contact has a company.

So I have a 'company' content type (name and logo), and I have a 'contact' content type which has a field which is a reference to a 'company'. This works smoothly.

What I want is to be able have a computed field in 'project' that displays the 'company' of the 'contact' ... in other words I create the 'project' and select the 'contact' for that 'project' and automatically compute the 'company'. (It doesn't have to update instantly, I just need to be able to display it.)

That's the easy bit (I think). Clearly this doesn't have to be re-computed every time the node is accessed.

I have to be able to display a 'project page' and display the company name and logo on that page, along with the project's contact name.

I know how to create a custom page I'm just not sure what to put in the page to get the company name and logo.

I have a vague idea (having read up on Computed Fields for CCK) of how it might be done but I could do with some direction.