Which star is the brightest for us. Not counting the sun?

Answer

The brightest star (other than the sun) is Sirius, main star of Canis Maior (Big Dog). This star is low in the south below Orion in winter evenings.
So this is about the “apparent” brightness, so the brightness seen from the earth. IN reality there are still stars that are much brighter (“absolute brightness”) but which we perceive as less bright due to their greater distance.