What would have been the typical drinks for a US farmer in the late 18th/early 19th century?

The time period of interest is entirely prior to the rise of the railways, and even to the construction of such infrastructure as the Erie Canal (completed 1825). Thus anything regarded as a typical or common drink would have been strictly what could be produced with local produce. Consumption of wines, beers, ciders, whisk[e]ys and other liquors and liqueurs from further than a few dozen miles would have been restricted to special occasions and wealthier individuals.

The main classes of alcoholic beverages that might have been available in the U.S. at this time are the following:

• (Grape) Wine: Made from fermented grapes.
  The well known varieties of Europe's vitis vinifera grapes do not put up well with North America's cold winters and hot summers, and the native North American grapes (bar hybridization) make an inferior wine. True wine aficionados will pursue making wine from any grape available, but the common palate is often unsatisfied with the result. The popularity of ciders in early North America is likely the result of the unpopularity of local wines.

• Ciders: non-grape wines

  Essentially the wine made from any fruit other than grape, such as apple, peach or pear; the former being the most prevalent. Their popularity in Revolutionary America is likely due to the non availability of quality wines at a low cost, providing inexpensive access to a low alcohol content beverage other than beers and ales. With both the falling transportation cost of European wines and the development of hybrid vinifera-labrusca grape varieties that both made a quality wine and could survive North American conditions, the popularity of ciders declines.

  The absence of truly satisfactory grapes for wine-making leads to a consequent absence of brandies (distilled/concentrated wines) except for the case of ciders. Apple-jack, traditionally made by jacking - allowing cider to freeze and discarding the ice to concentrate the alcohol - becomes a very popular drink in colonial America right through the 18th Century. It decreases in popularity through our period in step with the rise of American Whiskey. Other brandies are for the most part imported, and uncommon or rare until later in the 19th Century.

• Beers (Lagers and Ales): made from fermented grain, most notably barley
  Barley is a hardy grain, able to flourish in virtually any temperate climate, making it's fermented beverage a world-wide favourite. The "beers" made from grains such as rye and corn are also the base from which all whisk[e]ys are made by distillation and ageing. The ease and low cost of manufacturing it and the wide variety of climates in which the constituent grains can be grown mean that beer is always a popular drink.

  The distinction between ales and lagers is the temperature of fermentation, ales being warm-fermented and lagers cold-fermented. The different yeast varieties for these two fermentations usually result in ales also being top-fermented and lagers bottom-fermented, though this is not a strict distinction. The flavour distinctions between these two types of beers, and even their multitudinous varieties, would have been more typical of today's craft beers than of the mass-produced "fructose-beers" so popular across much of America post-prohibition. Extremely strong pride in local varieties should be expected, reminiscent of that displayed in the 1487 Leeuwarden beer riots.

• Whisk[e]y: Made by distilling and ageing a "beer"
  The distinction between whisky (Scotch and Canadian) and whiskey (Irish and American) is irrelevant to this question. They are all made by distilling a "beer" (the result of fermenting a grain mash) and then ageing the same in oak barrels. Corn whiskey or Bourbon in particular has long been a staple drink in the U.S., particularly in the Appalachian regions of the South East, as the corn used for its mash as well as the oak needed for its barrels is widely and inexpensively available.

• Gin, like whisk[e]y a liquor made by distilling a fermented grain mash, is predominantly flavoured by the addition of botanicals, particularly the juniper berry to yield its characteristic taste, instead of through oak aging. Prior to the development of modern distillation methods a few decades after our period it retained a distinctive malty character. This traditional style of gin is today branded as jenever.

  As with the whisk[e]ys there are many distinct varieties, but as the distinctions are more elaborate in origin than the originating grain I will not list them here.

  The strong juniper flavour typical of gins was found particularly effective in masking the bitter taste of quinine, leading to the popularity of gin and tonic in tropical climates susceptible to malaria and amongst those who had spent considerable time there. It would also have likely been popular in the New York City area due to its Dutch heritage, but less so elsewhere.

• Vodka: Originally, like the whisk[e]s and gins, made exclusively from grain mashes, by our time period vodka is also being made from starchy root vegetables such as potatoes and even carrots. They are distinguished by:

  • an over distillation to very high proof followed by dilution to the desired strength;
  • elimination of all distillation heads (ethyl acetate and ethyl lactate) and tails (fusel oils) that add distinct flavour characteristic to the gins and whisk[e]ys; and
  • flavouring with botanicals and other additives only after distillation.

  The result of this is to give a very clean alcoholic taste amended only by the carefully selected post-distillation additives, that requires no (and receives no benefit from) ageing of any sort.

  It's origins are in Eastern Europe - specifically Poland and Western Russia - and is only just spreading from those regions into Scandinavia during our period. It was likely very uncommon in North America until the mass migrations from Eastern Europe at the end of the 19th century.

• Rum: made by fermenting and distilling sugarcane molasses

  Originally a West Indian beverage, rum is already New England's most popular liquor when our time period begins, though it is a lighter product than typical in the West Indies - almost like a whiskey. During our time period rum declines in popularity as sugar from the West Indies increases in cost following the Revolution, and the development of American Whiskey varieties expands. One might even venture that American Whiskey is developed as an emulation of the light New England Rums. but distilled from grain mashes instead of molasses.

• Liqueurs: Highly sweetened distilled liquors of all sorts

  These are the co-base of most mixed drinks and c**ktails, softening and hiding the alcoholic flavour of the combining liquor. A development of the Medieval European monasteries, these were likely uncommon throughout the U.S. until canal and then rail transport became commonplace.

• Cocktails, mixed drinks usually made by combining a liquor with a liqueur or a sweet non-alcoholic beverage, are first attested in North America towards the end of this period. Our time period completely precedes the development of commercial non-alcoholic carbonated beverages by some decades, so the sweet co-bases would have commonly been fruit juices, or liqueur on a special occasion. However these really are saloon drinks, not beverages commonly consumed in the home or on the farm.

Returning to the question at hand, the most common and popular beverages were those that were inexpensive locally - which prior to the canals and railways was those that could be made locally from local produce: Ciders; beers and ales; corn whiskeys (Bourbon); and blended whiskeys. All of these could be made by many farmers themselves, from their own produce. As the vast majority of Americans were rural inhabitants until the end of the 19th century, these inexpensive local beverages predominated.

The easiest of these beverages to prepare at a lower alcoholic content, suitable for consumption by children and servants would have been small beers and small ciders at an alcohol content ranging between 0.5% and 3%, and unfermented ciders and fruit juices.

Note that it is quite possible to brew beer until the yeast dies of alcohol poisoning at 12-14% (depending on yeast variety) - as strong as any wine. In strength one would broadly distinguish between the small beers (up to about 3% ABV), table beers (roughly 3% to 7% or so ABV) and strong beers (above 7% or so ABV) with local regulations possibly providing legal definitions of the ranges.

Those seeking a stronger drink than strong beer or strong cider would have most commonly selected a New England Rum at the beginning of the time period, gradually shifting to an American Whiskey by the end. Both of the latter would have been much less expensive, throughout the time period, than anything imported from Europe, and offering a progressively wider variety of taste profiles as the period wears on.