The search-and-capture model of spindle assembly has been a guiding principle for understanding prometaphase for decades. The computational model presented allows one to address two questions: how rapidly the microtubule-kinetochore connections are made, and how accurate these connections are. In most previous numerical simulations, the model geometry was drastically simplified. Using the CellDynaMo computational platform, we previously introduced a geometrically and mechanically realistic 3D model of the prometaphase mitotic spindle, and used it to evaluate thermal noise and microtubule kinetics effects on the capture of a single chromosome. Here, we systematically investigate how geometry and mechanics affect a spindle assembly's speed and accuracy, including nuanced distinctions between merotelic, mero-amphitelic, and mero-syntelic chromosomes. We find that softening of the centromere spring improves accuracy for short chromosome arms, but accuracy disappears for long chromosome arms. Initial proximity of chromosomes to one spindle pole makes assembly accuracy worse, while initial chromosome orientation matters less. Chromokinesins, added onto flexible chromosome arms, allow modeling of the polar ejection force, improving a spindle assembly's accuracy for a single chromosome. However, spindle space crowding by multiple chromosomes worsens assembly accuracy. Our simulations suggest that the complex microtubule network of the early spindle is key to rapid and accurate assembly.