What motor type is better suited for instant torque supply
Permanent magnet synchronous motor (PMSM) would be a perfect choice if you have budget, otherwise a BLDC motor is also a good candidate. Stepper motors don't have a such high dynamics and short overload capability. Normaly PMSM is rated with 250% overload.
If you want a really good performance, then you hav to match moments of inertia, ideal is J_mot = J_load, if this is not possible then a reducer is used J_mot = J_reducer + J_load/P^2 , p is the reduction ratio.