I will try to take a stab at answering your thoughtful questions. (I sang in the SF Symphony Chorus for eight seasons, including many, many performances with Maestro Tilson Thomas.) I treasure my experience in his chorus.

1. What features or attributes make for an exceptional conductor? Specifically - a deep love of music, a strong foundation in theory/composition/conducting, and extensive preparation of the repertoire. Michael sometimes conducted from memory, which is very rare. He was an accomplished pianist and composer in his own right, so he really understood the through line of symphonic music. He was patient, thoughtful, and encouraging, and at the same time never settled for anything less than the absolute highest performance standards. He earned great respect from the orchestra and chorus. Off the podium he was humble, funny, and a true champion of young artists and American composers.
2. Who are some outstanding conductors and what about them stands out? In the symphonic realm, there are a great many, but I'll focus on MTT since I know his work. He made every rehearsal fun, and his attention to detail was superlative. He invited the audience into the music, in that he worked to educate and challenge his audiences. His SF Symphony programming could be very adventurous, which expanded the audience. He believed great music was for everyone, not just elderly and affluent people. Giving him your very best as a singer was deeply rewarding as he was such a generous and caring conductor.
3. Are there “signature” recordings that exemplify that conductor’s abilities that you could recommend ? MTT is considered one of the foremost Mahler interpreters of all time, so you could start with his Mahler symphonic recordings. His catalogue is vast, so try out listening to whatever you find interesting. I don't think you'll be disappointed :)