We’re working on some improvements to material editing in SketchUp for Web, including removing and editing single materials.
In the near term, the current method for adding a material is to click the File Icon > Insert and import an image as a material.
Can you clarify what you mean by ‘basic material’? Since you also ask about applying one material to the entire model I wonder if you are talking about monochrome face display. Monochrome face styles are a quick way to apply one material to all faces in a model, and the nice part is that you can still use the entity-specific materials you apply.
With a Shop subscription, we include Style editing that allows you to specify a default color for front faces in monochrome styles. Open the Styles utility and hit the edit icon next to the Style thumbnail. Then, go into face settings to edit the default material.
If you are using SketchUp for free, there are a few styles like Hidden Line that are set to monochrome face display.
I hope this helps get you oriented. We’re working on a few things to make this a bit smoother.