Smirnoff's amazing marketing decades ago, along with a really weird decision by Ian Fleming for what 007 would like to drink, these things were the biggest reasons why Martinis went the way of flavorless (vodka instead of gin, dry vermouth instead of sweet). Another marketing ploy by Smirnoff include the use of copper mugs for the Moscow Mule (which is really how Americans got introduced to vodka). Not a Russian thing, completely a Smirnoff invention. Rant aside. I believe the term Martini originally came from the Martinez, which was named after the city in CA. It's basically a Martini (gin instead of vodka, sweet vs dry), but the difference is the touch of Maraschino liqueur. Robert Hess does 2:1 vermouth:gin, but most people prefer 1:1. Try Plymouth Gin, or perhaps an Old Tom gin of some sorts. Ok thanks for letting me rant.
I think maybe a smooth Pilsener or lager to start with? Maybe don't jump right into the crazy high IBU beverages created by the mad scientists of San Diego. Not to make it seem more difficult, but the glassware and temperatures can sometimes be a pretty big deal. I think Carlsberg from a Carlsberg glass is stupid smooth. The Paulaner stuff like the Pils and Hefe are very smooth too, IMO. Never straight from the bottle, if you care, use a good glass.