Twisted double bilayer graphene (tDBG) has emerged as an especially rich platform for studying strongly correlated and topological states of matter. The material features moiré bands that can be continuously deformed by both perpendicular displacement field and twist angle. Here, we construct a phase diagram representing of the correlated and topological states as a function of these parameters, based on measurements on over a dozen tDBG devices encompassing the two distinct stacking configurations in which the constituent Bernal bilayer graphene sheets are rotated either slightly away from 0° or 60°. We find a hierarchy of symmetry-broken states that emerge sequentially as the twist angle approaches an apparent optimal value of $θ≈$ 1.34°. Among them, we discover a sequence of symmetry-broken Chern insulator (SBCI) states that arise only within a narrow range of twist angles ($≈$ 1.33° to 1.39°). We observe an associated anomalous Hall effect at zero field in all samples supporting SBCI states, indicating spontaneous time-reversal symmetry breaking and possible moiré unit cell enlargement at zero magnetic field.