Here's the list of what each type of alcohol costs and how much intoxication "credits" you get for each one.
You can get the following at both the Green Man Tavern and the Sailor's Den in OT.
Alimane Red - 50c - 1 unit
Asgardian Stout - 1s - 2 units
Bossonian Brandy -25s - 4 units (can't drink more than one of these while intoxicated)
Grog - 20c - 1 unit
Liquid Starlight - 1s 50c - 2 units (this sounds like something from WoW)
At the Purple Carp Tavern in Khemi, instead of Liquid Starlight, you can buy Serpent's Tears.
Serpent's Tears - 50c - 1 unit
So millions of pirate jokes can't be wrong. Grog is the drink of choice for the frugal drunk.
At both the Rum n' Rumble in Tortage and the Armsman Tavern in The Noble District anyone with a drinking cape can get Ambrosia, which provides 2 units of intoxication, for free.
To receive the hungover Achievement, start the drink that will push you to 10 units before finishing the previous one.
You can also stop the staggering by unsheathing your weapons. Because everyone loves an angry drunk.