Serving a drink in the appropriate glassware is important.
Martini glasses, coupes, and various other cocktail glasses are best for drinks served up, without ice. Often, modern martini glasses are comically large; try and find older-styled ones which are generally shorter and with a smaller bowl, ideal for holding traditionally-sized drinks. Any sort of stemmed cocktail glass with a modestly-sized bowl will do. These glasses should never serve drinks over ice, only neat, and it is best to keep them in your freezer prior to use.
Lowball glasses, old fashioned glasses, and rocks glasses all refer to short glasses good for serving spirit-forward cocktails over ice as well as neat spirits or spirits “on the rocks”. Double old fashioned glasses are larger and are good for serving drinks over ice that have a lot of liquid volume, such as the Mai Tai.
Anything intended to be served up, in a cocktail glass, may also be served in a lowball glass with ice. For stirred cocktails, a single large cube or sphere of ice would be preferable if translating the drink into an “on the rocks” lowball drink. For shaken cocktails, regular cubed ice should be fine. The inverse is also true; a drink meant to be served on ice may instead be served up in a chilled cocktail glass. Double strain any shaken drinks, if serving them up.
Highball glasses and collins glasses are taller glasses used to serve highballs and “collins” drinks, respectively. Collins glasses hold a bit more volume than highball glasses. These may be frozen or chilled before use.
Specialty glassware includes margarita glasses, absinthe glasses, champagne flutes, and various snifters, among others. These can be acquired on an as needed or as desired basis. Cocktail glasses of your preferred style, old fashioned or double old fashioned glasses, and highball or collins glasses should be fine for almost all uses.
For casual outdoor use, a good set of acrylic table glasses is preferable.