During Prohibition, my grandfather bought cans of industrial ethanol from his bootlegger. He poured it in his bathtub, added an equal amount of distilled water plus a little extra and a little syrup of juniper, angelica and coriander, and then he bottled his bathtub gin. It was the worst gin anyone ever tasted, really terrible but no one drank it neat. They added things to kill the taste and that is how gin cocktails were born. There are more gin cocktails than you could shake a stick at.
I use London dry gin for cocktails. Beefeater is distilled in London in copper pot stills not column stills — that's the bottom line — and since I live in a former British colony, I can buy 94º proof Beefeater. It is frequently on sale. The UK has (or had) crazy liquor laws, and all gin has (or had) to be sold at 80º proof. That's ok for Plymouth Gin and Old Tom Gin which are meant to be served neat, but IMO it is too weak for cocktails.
Broker's London Dry Gin is distilled in Manchester in copper pot stills and it is good enough to drink neat, but it costs more than Beefeater. It is capped with a bowler hat like a London stockbroker and those plastic bowler hats look great on dolls.

My favorite gin cocktail is a Negroni: one ounce gin, one ounce Campari, one ounce red vermouth, on the rocks with an orange slice. It is wonderful just like that. Extra gin for a "stiff one" gives it a horrible medicine taste, so make a double if you want a stronger Negroni.
Gin and tonic is a legacy of the British Empire. Imperial soldiers and civil servants in the malarial zones were supposed to drink quinine water daily to keep their fevers down. They didn't like the taste, and hence arose the custom of improving it with a shot of gin.
Any gin cocktail that you shake with egg white is a hangover cure. I always stop at one drink, so I don't have hangovers and I never tried a cure: but a New Orleans gin fizz sounds like a better drink than beer and tomato juice.