Thor's goats actually presented the connection between Thor and humanity as well as Thor's natural strength. 

Thor's goats were named Tanngrisnir and Tanngnjóstr.

We don't know how Thor picked the pair. What we have from Norse mythology is that Thor owned this pair of goats. That's it. 

Thor's goats presented Thor's connection with people in Midgard. 

In recorded history, goats have always been constant companions to people all around the world. Goats first became domesticated about 11,000 years ago. Goats could provide many types of necessities like fur, milk, meat, bones, skull, etc. A goat meant abundance as well as presented its closeness with humanity.

Goats in Norse mythology presented protection, physical strength, abundance, and blessings. 

Thor often brought people in Midgard with blessings and fortune as well. In Norse mythology, Thor defended those who believed and worshipped him. He often turned up in formal ceremonies like birthdays, funerals, weddings, etc. to offer his blessings. Compare with gods like Odin or Freyr, Thor had better bond humanity. He communicated with Midgardsmen or even had dinner and slept in a house of Midgardsmen as well. 

If the horse Sleipnir of Odin the Allfather presented the leadership and the pioneering force in battle, goats of Thor presented the commonness shared by Thor and humanity. Sometimes I feel like a pair of goats was what made Thor become "humanized" and friendly among Midgardsmen. 

Moreover, a pair of goats presented the physical might of Thor as well. Scandinavian goats often give us the feeling of more muscle and strength than goats from other parts of the world. And maybe because of this, Thor's goats became the symbol of Thor who was considered among the mightiest gods in Norse mythology.