Half the fun of cocktails is making little twists to the established basic recipes. I love a Manhattan and am amazed how much changing just one ingredient changes the drink.
For a group of base recipes, I actually use this list:
https://en.wikipedia.org/wiki/List_of_IBA_official_cocktails
Each cocktail there has the IBA "recipe" which is the standard upon which they base their judging in their World Cocktail Competition.
My only other suggestion is to not try to stock a new bar for a dozen different cocktails. It's tempting, but can get very expensive to start but can also see you buying spefici liqueurs and flavorings that are only used in one drink that you might make once in a rare while. Buy your base liquors (vodka, whiskey, gin, etc.) which can be used for all variety of drinks. From there, think of two or three cocktails you know you are going to want to drink and buy the specialized ingredients for those (vermouths, bitters, etc.). With the basics in hand, you can easily expand out to others, but starting with a core group will help conserve the budget a little.
Glassware is also very nice, but can also get expensive. You see all variety of glasses here, but my recommendation is to
not do what I did and buy a bunch of specialized glasses I never use. Rocks glass, Collins glass, and Highball glasses are not terribly different than the glasses you probably already have in your cupboard. Use those to start, then get the "proper" glassware as you settle in. Something like a Nick and Nora glass (I prefer to the V shaped Martini glass) doesn't really have an equivalent in your cupboard already but you could get away with the "wrong" glass if drinking for yourself for a little while until you learn you are going to be making more of the drinks that feature those.
Pony/jigger, shaker and other bar hardware (and even some simple glassware) can be had relatively inexpensively if you have a restaurant supply store where you are at.
Good ice makes all the difference. If your water at the tap is a little funky, make ice from filtered water. You'll go through more ice than you think when making cocktails.
Good luck and enjoy the ride! I had
plenty of time to explore cocktails during COVID lockdown and looked forward to ordering my next batch of ingredients so I could play with a different rye here or vermouth there.
