Quiet & steady, well trained but tolerant of beginner mistakes. I prefer a beginner horse to have all of the buttons available for a beginner to use as they progress/learn them but not so sensitive that they create a problem prior to that. A horse that goes where asked, when asked and at the speed asked.
Something with a bit of age and lots of miles.
Absolutely no vices or behavioral issues. Having things to fix, even if minor, can be very daunting for a beginner owner & rider. Those kind of things can make a beginner frustrated and lose interest.