Water tumblers are the workhorse: short, stable, and dishwasher friendly. Buy six to eight for a household of four.
Stem wine glasses keep hand heat away from wine if a bottle sits through dinner. Rocks glasses suit whiskey and short cocktails. Highball glasses fit iced tea and gin and tonics.
You do not need every shape on day one. Start with tumblers, add stems when wine is a regular part of meals, and add one or two rocks glasses if you mix drinks at home.