Alas, I was spoiled by having traveled to Russia a few years back and getting to try the real thing. The brands available in the US (even the expensive ones) don't taste very good to me any more.
However, I would go for Absolut, Finlandia, or Skyy. They're all much more agreeable than Smirnoff or similar lower-shelf things. If you are mixing drinks from recipes, do not use the flavored vodkas unless specifically called for, or you feel adventuresome. Since vodka itself is essentially flavorless, most mixed drinks that use vodka depend on that fact, and the other ingredients are chosen so as to produce the desired flavor.
BTW, a properly made martini is not much different from straight shots of gin or vodka. If you're not into taking spirits straight, you'd be better off looking at cocktails that use liqueurs, soft drinks, fruit juices, etc.