It seems that rectangular coordinates in Earth-centered inertial frame is a viable choice. The relative spherical coordinates may be susceptible to singularity during the lift-off (i.e initial conditions such as velocity and flight path angle are 0 m/s and 90 degrees, respectively).
From page 42 of Ezgi Civek Coskun's 2014 Ph.D. Thesis Multistage Launch Vehicle Design with Thrust Profile and Trajectory Optimization:
Knowing the fact that Newton’s laws are valid only with respect to the inertial frame, it is the easiest and the fastest way to define and integrate the equations of motion in Earthcentered-inertial (ECI) frame. And also, rectangular coordinates are preferred since they offer a simpler formulation and eliminate singularity problems at lift-off (zero initial velocity and 90° flight path angle).
While on the other hand, the relative spherical coordinates give a better insight and understanding about the vehicle’s motion, so they are used as the output coordinates to present the results to the user. Furthermore, since the final state of the launch vehicle’s ascent trajectory is defined with respect to the orbital frame, it is also required to compute the orbital elements all along the trajectory in order to assess whether the terminal boundary constraints are satisfied or not. Different coordinate systems and the related transformations between them are presented in Appendix B.1 and Appendix B.2, respectively.
Although the rotational dynamics are not modeled in the equations of motion, the attitude of the launch vehicle can be defined based on certain simplifying assumptions, and thus trajectory control variables can be physically interpreted easily. The attitude, in general, describes the orientation of a body-fixed reference frame with respect to an external reference frame. Euler angles or aerodynamic angles are often used to specify the attitude of the launch vehicle during flight.