Potato vodkas are naturally smoother than grain for the most part. (Which makes them better for martinis. Mixed drinks being smooth really doesn't do much) For instance, a bottle of Molopola (sp) cost around $10-$12 last time I checked, and it is a lot smoother than Grey Goose at $40+.
One grain vodka that is very smooth is Absolute.
Go to the liquor store and as for a potato vodka and just buy the $9-$14 bottle. You won't be disappointed.
If you want a better martini, buy Tankaray TEN Gin. It makes the best martinis.