Product pricing question

Hello,
I'm working with a customer that wants to add custom handling prices to classes of products within their store.

e.g.
Product A is of Type 1
Product B is of Type 1
Product C is of Type 2
Product D is of Type 3

During checkout, the Type of the product needs to be evaluated to see which type it is to add the handling price. Type 1 overrides Types 2 and 3 (if a product of Type 1 is in the cart, then handling would be that much).

Is this something that I can do with product attributes? I've messed with it some, but it seems to get messy. I would like for my customer to be able to easily add an attribute to all products of Type 1, but I can't figure out how to do that.

Any thoughts would be quite welcome.

The easiest method would be to add a new field to the products table for something like:
products_shipping_type

and then this can be evaluated to see if it exists in the shopping cart for each of the various types and based on what is found add the separate handling fee that rulez ...