Home bar guides tend to list forty bottles and twenty tools, which is both expensive and unnecessary. A small, considered setup makes better drinks than a large unfocused one, and it takes up far less space.
The most common mistake is buying a bottle of everything because a list said to. Most of it sits unopened for years while the same three drinks get made.
The better approach is to identify two or three cocktails you actually enjoy and buy for those. A negroni needs three bottles. A daiquiri needs two plus limes. Building outward from drinks you will make produces a bar that gets used.
Ice is the ingredient people underestimate, and having it available in quantity and kept cold changes the drinks considerably. Insulated buckets and barware, of the kind catalogued at https://oggi.us.com/, handle the part of hosting that is logistics rather than mixology.
Bartenders measure every drink, including ones they have made thousands of times, because cocktail balance is narrow. A quarter of an ounce more citrus is a noticeably different drink.
Free pouring is the single largest difference between a home drink and a bar one, and a jigger costs very little.
Small, wet ice from a domestic tray dilutes fast and produces watery drinks. Larger, denser cubes dilute more slowly and keep the drink cold longer.
Silicone moulds for large cubes are inexpensive and make a visible difference to spirits served over ice. For shaking, plenty of ice is better than a little, since more ice chills faster with less dilution.
Simple syrup is equal weights of sugar and water dissolved, keeps refrigerated for weeks, and is far better than any commercial substitute.
Fresh citrus is non-negotiable in anything that calls for it. Bottled juice tastes of the bottle, and the difference is immediately obvious in a sour.
Spirits keep indefinitely unopened and for a long time opened, though anything low-proof or containing sugar degrades faster once opened. Vermouth is the classic case: it is wine, it oxidises, and it belongs in the refrigerator after opening rather than on a shelf for a year.
Keep bottles out of direct sunlight and away from heat, which is the usual argument against storing a bar next to a radiator or in a sunny window.
Adding a bottle when a drink you want requires it produces a bar that reflects what you actually make. Buying comprehensively at the start produces a shelf of things you do not.