Among Cylindrical / Mercator / Spherical the best projection mode is the one you like better when applied to the particular subject you chose, the particular framing you select, etc.
The best way to decide is to try them, especially when you find something being too stretched or too squashed with the mode APP selected. As the following screen captures show, Mercator is "somewhere between" Cylindrical and Spherical.
Comparison with Planar are less straightforward because the Center Point placement plays an important role for Planar (aka rectilinear) projection.
For 360° x 180° the only option is Spherical, but for 360° where height is limited, any of Cylindrical / Mercator / Spherical is worth trying.
Don't be afraid by the mode names or the underneath math, click and enjoy!