A working home bar is five bottles, not thirty: vodka, gin, white rum, bourbon and tequila. That five covers most of the world's classics. Around them — the supporting cast you buy as needed: tonic, soda, ginger beer, fresh limes and lemons, simple syrup (sugar and hot water, one to one).
For tools, start with a jigger, a shaker (or a jar with a tight lid), a barspoon and a freezer full of ice. The jigger matters most: drinks fail on free-pouring, not on cheap spirits. The full equipment list with honest substitutes lives in the Guides; the five-bottles-to-ten-cocktails route is in the blog.
Homework: assemble your five (two bottles count as a start), tick them in the site's bar finder — it will show what you can already mix.