A variant of the Manhattan — and a precursor to the Martini — the Martinez was a very popular drink in the pre-Prohibition era, utilizing one of American’s favorite spirits: Old Tom Gin.
Old Tom Gin was a slightly sweetened gin that was popular in mid-19th-century England. It soon made its way to the States, where it became a common cocktail ingredient in the latter part of the century. Eventually it fell out of favor and was replaced by London Dry Gin, popularized by such brands as Tanquery and Beefeater.
Old Tom Gin can be hard to find, but there are a few different brands on the market if you keep your eye out. Hayman’s is probably the most common. There are also Old Tom Gins from Ransom, Spring 44, and Jensen, none of which I’ve tried. (Tanqueray is scheduled to release their own version of Old Tom Gin imminently, which has cocktail folks very excited.)
If you don’t have any Old Tom Gin, you can substitute another style of gin. Something that is not too junipery — like Aviation, Caorunn, or Citadel, for example — would be a good choice. Or you can try it with Genever.