I know that blue stars are the hottest and youngest (according to Universe Today). But what makes them blue, instead of other colors like purple?
Our eyes and brains make them blue.
Stars are (close to) a black body, they emit a broad band of radiation. The hottest stars will emit most of their radiation in the ultraviolet but they will still be very bright in visible light.
As they get hotter, they emit even more ultraviolet, and more visible light but the mixture of wavelengths in visible light doesn't change much.
This mixture is interpreted by our brains as being a sort of light blue. No matter how hot the star gets, it will still be emitting lots of visible light in a mixture that looks "light blue". It will never look purple.
Purple can only be seen if either a single short-wavelength visible light is being emitted, or a mixture of short and long wavelengths (red and blue). Neither of the mixtures can occur in light emitted from a black body.
So stars can appear red, orange, yellow, white or light blue, but never green or purple.