My top 3:
The Negroni - equal parts gin, campari, sweet vermouth. personally i prefer it a little more like 2-1-1 gin forward. it's bitter and boozy that clears the palate and makes for a good pre-dinner drink. any decent bartender should know how to make this.
The Boulevardier - same thing except whiskey instead of gin. a little rounder and fuller flavored. i actually prefer it. this is my goto.
The Last Word - another classic cocktail. equal parts gin, luxardo cherry liquor, chartruese, lime juice. sweet and boozy. a little tougher to make as chartruese is harder to find, but a real bar will have it.
here's a cocktail list i put together for my home. i got tired with asking people if they wanted a cocktail and hearing, "sure, what do you have?". it helps guests pick something based on ingedients i have on hand and flavor profiles they can understand, it keeps recipes handy, and it gives me something to use for an inventory checklist. they're also all pretty classic and well known drinks (except for the mono pequeno which is something i made up for my wife).