e-commerce taxonomy menu

I am challenged & need assistance.

Novice Drupal user, have created a taxonomy structure, vocabularies (about 5), each with 3 to 20 terms, each term with 3 to 40 subterms.

I then create products, there may be 250+ of these.

Each of the products need to be "tagged" with 3-30 sub-terms and the parent term.

The tags, together with other links such as "read more" and "add to cart" display after the item subject. If the number of tags is more than 4, the tags and other links run into each other.