Depends on the project, but:
Poster board in several colors
Shoeboxes. Keep several around and keep the lids. These are great for small dioramas. I never throw a shoebox away!
Construction paper.
Glue sticks. If you only have liquid glue, be sure to have good quality glue sticks. Elmer's is good. Cheap brands are lousy and worthless.
Model Magic. This is made by Crayola. It's a kind of modeling clay and is expensive ($3.99 for a small pack of one color here) BUT it works very well for making figures for dioramas, for instance. Be sure to store it tightly wrapped in sealed bags once you open it. Worth stocking up if there is a sale or coupon. It dries and is far better than Play-Doh or cheap modeling clays.
Keep popsicle sticks (called craft sticks at craft stores) and things like wooden coffee stirrers from the coffee shop around. Great for dioramas and projects but also for stirring liquid glue or paint, spreading glitter glue, etc.
Those are some of our basics. I would not over-buy things since each assignment can be different. It will be fun for your son to work on a list of supplies for a project and go to the craft store with you. But...yes, get those good glue sticks and some Model Magic on sale when you can! They'll keep!