The highball glass is probably the most used type of drink glass nowadays. Usually it holds around 7 fl oz. (200 milliliters). A Collins Glass is a kind of highball, a bit taller and more slender.
The smallest glass in the family is mainly used for serving. It can also come in handy as a measuring glass as it holds 1.5-2 fl oz. (40-60 milliliters). Sometimes called a shooter or a pony glass.
If you have a freezer at hand, you can skip chilling your cocktail glasses with ice. Shooters and rocks glasses are nice to have pre-chilled too. A chilled glass keeps cocktails crisp and cool longer, and adds aesthetics to the final presentation. Even if you only do a quick chill you will never regret it.