How do I build the best Spaghetti Bridge?

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It is nice to have a list of materials.
The thing which is missing is the goal. What is the bridge crossing? What is the problem being solved? What makes one bridge better than another?

most stable? holds the most weight? Spans the greatest distance? Highest strength to weight ratio? Tallest? Most ornate? Most colorful?...etc.

The best results are going to come from working as a team. The countless hours put into research, design, development and testing will also be useful.

A pasta bridge competition sounds cool.
I have little doubt that there are not hundreds of Youtube videos showing what works, and what does not help.

Personally, I'd try something new and different.
Idea 1: Treat the unlimited pasta as a raw material. Why not grind up the pasta into say flour, then see if you can cast a flour/water mixture into structural components? Maybe cast pasta pieces are stronger than regular pasta shapes? Maybe pasta can be re-extruded into I beams and C channels? Maybe the liquefied pasta could be cast into forms like concrete?

Idea 2: Can anything be done to pasta to increase its performance? Materials are always being improved with treatments like coatings, heat, cold...etc. Experiment and see if pasta can be improved. How is the strength of pasta affected by its moisture content? Is one brand stronger than another?

Idea 2a. It is certainly against the rules, but make plated pasta. It is not very difficult to plate even non-conductive materials with copper, then apply a few thousandths of nickel.

Idea 3: What are the material properties of cooked pasta which is then allowed to dry out? You could create some lovely organic shapes with cooked pasta, then allow it to dry, and it would keep the shape. Organic shapes are often stronger than "engineered" items out of structural stock. It might be worth some testing.

Idea 4: Use the other materials in "inappropriate" ways. Wooden blocks can become sawdust. 2 liter PP bottles can be remolded into more useful shapes via injection molding. Wood and polypropylene raw materials can then be used to form things like joints, gussets, hinges, or other materials not provided.
The same goes for the nails. Styrofoam can be reduced to rather effective "glue" to help hold things together.

Consider this contest like living in the Matrix. There are rules, but using those rules to your advantage is how you succeed.