BBR - Ball-Balancing Robot design

I have seen several posts here and YouTube videos about Arduino powered Ball Balancing Robots, but all are several years old at this point.

Does anyone have any motor suggestions for a small (18" tall) BBR design, and the pros/cons of basic DC motors vs. stepper motors vs. brushless motors on a project such as this?

DC: most power when at speed.
Stepper: most power when slow.
Brushless: depends on what you buy.