Most vodka today, and much (if not most) vodka historically, is grain vodka, mostly distilled from rye, wheat, and barley. Some is or has been made from oats, and some historical vodka was apparently distilled from buckwheat if you want to include buckwheat as an honorary grain. Some modern vodka, mostly from southern Europe and the US, is distilled from maize.

The early history of vodka is sparse, and there is no general agreement on origins (at least partly due to nationalistic argument between Polish and Russian historians as to who should take the credit (blame?) for its invention. While some Polish historians push for an origin at early as the 11th century (in Poland, of course), based on a beverage called gorzalka, implying inflammability, it is generally believed that widespread north European production of distilled drinks only dates to the late 14th century. Certainly, in the early 15th century, vodka was being produced in both Poland and Russia. If we broadly classify "vodka" as north European neutral spirits, then we should also consider the origins of Brännvin, Schnapps, viina, etc. Putting aside the vodka origin wars, it was present a good century before Columbus, and 300 years before the potato became common in Europe, and made from grain (and buckwheat). Later additions to the agricultural repertoire added maize, the potato, and sugar beet molasses to the range of fermentables. if we extend "vodka" to include East Asian distilled neutral spirits, then Korean soju and Japanese shochu and Chinese baiju are candidates; these are made from various ingredients such as sorghum, sweet potatoes, rice, and potatoes (and probably also wheat and barley, but these are less common).

We don't know how much vodka was made with potatoes historically, since a lot of vodka (and perhaps still the majority today) has been made for local consumption, tax-free (and therefore often illegally) and unrecorded. The potato might well have made "local" vodka more common and cheaper, but even without the potato, there would have been vodka (and probably a vodka problem).

Before distillation, whether that arrived in the 11th century or the late 14th, North Europeans drank mead (or other fermented honey drinks), beer, and imported grape wine.

For a reasonable overview of the history of vodka, see:

• Patricia Herlihy, Vodka: A global history, Reaktion, 2012.

The early history is covered briefly, since we have few sources. There is also*

• William Pokhlebkin, A History of Vodka, Verso, 1992.

which "proves" the Muscovite origin of vodka, and gives a lot more detail, although not always reliable, on the early history of vodka. (I haven't read this book yet; I'm just passing on what some scholarly reviews have said.)