* Largest by diameter: The largest star we know of is UY Scuti, a red supergiant. Red supergiants are indeed red, as their cooler surface temperature (around 3,500 Kelvin) emits mostly red light.
* Most massive: The most massive stars are also often blue supergiants, which are incredibly hot (around 30,000 Kelvin). These stars emit a lot of blue and ultraviolet light, making them appear blue.
So, it depends on what you mean by "biggest"!