the blue giant is the brightest star
Altair is the brightest star in the constellation Aquila and twelfth brightest star in the night sky . It is an A- type main sequence star
Betelgeuse is the ninth brightest star in the night sky and second brightest star in the constellation of Orion.It has a spectral type of M2 and is a red supergiant.See related question for more information.
Virgo is a constellation, not a star. The brightest star in Virgo is Spica, which is a blue giant.
A beta star is generally, but not always, the second brightest star within a constellation.
Alpha Carinae (Canopus) is the brightest star in the southern constellation of Carina and Argo Navis.It has a spectral type of F0 and is a white star.
Beta Cancri (Tarf) is the brightest star in the constellation Cancer.It has a spectral type of K4 so it is a orange giant.
Spica is the brightest star in the constellation Virgo.It has a spectral type of B1 and has a temperature of 22,400oK
Sigma Sagittarii (Nunki) is the second brightest star system in the constellation Sagittarius.It has a spectral type of B3 and is a blue giant.
It is the brightest type of star, Red Supergiant.
Beta Leonis (or Denebola) is the second brightest star in the constellation Leo.It is a type A3V star. This means it is very hot 7,500 -> 10,000 Kelvin and will appear as white.
There is no star that is simply called "Alpha". There are several that have "alpha" in their name, for example Alpha Centauri, Alpha Cruxis, Alpha Canis Majoris, etc. - usually the brightest star in each constellation. Some stars such as Betelgeuse (Alpha Orionis) are not actually the brightest star in the constellation.
Alpha Cassiopeiae (Schedar) is the second brightest star in the constellation Cassiopeia.It is an orange giant star with a spectral type of K0.See related link for more information.