How to structure many-to-many categories relationship

I’ve seen several inquiries about this, but can’t find a definitive answer: What is the best way to structure a many-to-many categories relationship in WordPress?

The site I am building is not a shopping site, but it does have product types and brands that I need to connect. One product category has many brands, and one brand can be listed under many product categories.

When designing a ‘regular’ database, I would create a linking table called, “product brands.” Is there a way to mimic or actually build a linking table in WordPress?

Would it be best to use custom taxonomies? Or the post-to-post plugin? Or is there another/better way? (I’ve never used custom taxonomies, so please use as much beginner language as you can if this is the case ??

The theme I am using is Suffusion, if that makes a difference.