The most important aspect of an emerald is it’s color. The colors are graded based on the stones hue(the shade of the color) the saturation(the intensity of the color) and finally the tone(the lightness vs darkness).
Next is the clarity emeralds are a type 3 stone meaning they are always included.
So when picking your stone in terms of clarity you are looking for straight lines that match the shape of the stone and also that the inclusions are not blocking or interfering with the stones color.
Emeralds come in lots of shapes usually they are cut in emerald cut because it protests the stones corners from chipping because emeralds are very soft but any cut will be fine as long as it is set carefully.
Lastly, when picking your ring you must make sure that the design is something you love because changing it afterwards can be risky as the stone can break.