Your pet is important! Visiting them sets your mood to Bold (hawk), Indulgent (viper) or Negative (blob/maw of darkness). Since in between the social phase and selecting next turn's classes you have the mood picker, this actually means that:
- with the hawk, you can reach the Daredevil and Determined moods on the next turn, and Bold, Excited, and Secretive in two turns
- with the snake, you can reach Compliant and Social on the next turn, and Indulgent, Excited, and Cautious in two turns
- with the blob, you can reach Cautious and Secretive on the next turn, and Negative, Compliant, and Determined in two turns
Since winning people over is such a large part of the game, the Emotion and Interaction skills are very important. Emotion is boosted by Indulgent and Social, and Interaction is boosted by Compliant and Social. So I'd recommend the snake for a first run—it makes it much easier to build up those social skills!
You may be able to unlock a way to set your mood to Compliant in the same way as visiting a pet—you'll be able to reach Indulgent/Cautious the turn after, and Social, Negative, or Compliant again in two turns. If you manage to do this in a hawk pet run, you'll be able to reach any mood on the wheel in two turns, which gives you a lot of flexibility in learning.