What should the mass of a planet be in-order for its escape velocity to be near the speed of light? What should the mass of a planet be in-order for its escape velocity to be the speed of light?  Is it even possible? What will it look like from an outside viewer? Will it even be visible in the human eye spectrum?
As @KeithMcClary says in his comment, escape velocity depends on both mass and radius. The smaller the radius for a given mass the higher the escape velocity. So if you could somehow compress the Earth until it was just a few centimeters across, its escape velocity would approach the speed of light.
At the other extreme, if you filled a space twice the diameter of Earth's orbit with copies of the Earth, without doing any compressing at all, it would already be a black hole.
If you just pile matter onto a planet and let its own gravity compress it, you need about 2 solar masses before it is close to being a black hole (at which point it is 10-20 km across).