So, today we had our next session. After getting her Pokemon back from Nurse Jenny, she spent $10 buying a Pokeball. She then went back out of town to see if she could find any wild Pokemon. She drew a Diglet from the random Pokemon pile. Using a Pichu to weaken it she managed to catch it without issue.
She than ran into the same trainer from the last session who gave her info on the Tori Gym Leader and her contact info (she put it in her fake phone) to contact her for future battles (similar to what you see in Gold/Silver).
Upon return to Tori Town, A. went straight to the gym and challenged the gym leader, Feza.
He had a much stronger Pokemon, a Pidgeotto, which knocked out her Pichu and Rattata. They did just enough damage, though, and she finished off Feza with her Pidgey to earn the Wing Badge and $50.
She finished the session by returning her Pokemon to the Pokecenter for healing.