If you are in Draconic Arts, you will choose from the Riding Dragons. During the second year, you may get a pet from any category.
If you are in Traditional Magics, you will choose from any category except Riding Dragons, Ancient Ones and Sea Dragon. During the second year, you may get a second pet from any category.
If you are taking both courses, you will choose one each of the above. You may not have another pet during the second year.
I hope this answer your question. Any other questions?