I'm particularly interested in Thomas Jefferson and George Washington. I found a recipe online which apparently was written by George Washington. Also, I read that Jefferson and Madison wrote to each other about beer and even a federal brewery. I would love to know more about the styles that were brewed by these men.
The primary styles brewed commercially during this time would be British style ales and porters, but most beer brewed in the home would be "small" or "table" beer, meaning it was only about 1% and meant to be consumed with meals (as in any meal, even breakfast).
Jefferson preferred wine to beer most of the time, though. While serving as Secretary of State there are records of him purchasing bottles of porter, likely for entertaining, and twice in 1798 he purchased hops, possibly for his servants to make small beer.
After 1813 Jefferson began trying to brew at Monticello (there's no evidence he ever sold what was brewed there) with the help of a British maritime officer, Captain Joseph Miller, who had previously worked in a brewery and would later teach Peter Hemings, one of Jefferson's servants. In 1820 he did discuss the brewing process (for private, home use) with James Madison and, in 1821, discussed Monticello's production in a different letter:
we brew 100. gallons [1 keg = 32 gallons by modern definitions] of ale in the fall & 100. gallons in the spring, taking 8. gallons only from the bushel of wheat. the public breweries take 15. which makes their liquor meagre and often vapid.
I take that last part to mean Jefferson's servants used more malt, making the beer richer and less watery.
As for a federal brewery, I didn't find anything to suggest Madison and Jefferson discussed that specifically. But a man named Joseph Coppinger, who was then publishing a brewing instructional book, did write to then-President Madison touting the concept of a national brewery which would improve the quality of "Malt liquors" (beer), serve as a moral and healthy alternative to distilled spirits, and be enormously profitable to boot. This letter reached Jefferson's hands. When 1815 came around and Coppinger still hadn't let it go, Jefferson had this to say in reply:
I have no doubt, either in a moral or economical view, of the desirableness to introduce a taste for malt liquors instead of that for ardent spirits. the difficulty is in changing the public taste & habit. the business of brewing is now so much introduced in every state, that it appears to me to need no other encouragement than to increase the number of customers. I do not think it a case where a company need form itself on patriotic principles meerly, because there is a sufficiency of private capital which would embark itself in the business if there were a demand, but as to myself particularly I am too old & too fond of quiet to engage in new & distant undertakings. [though Jefferson was brewing privately in Monticello during this time.
I think Jefferson's being a bit generous here, as in 1810 the US had only 132 breweries nationwide, with a combined output of less than just one of the major London breweries at the time (about 200k bbls).
I haven't looked up Washington yet but I'll post again if something interesting pops up.
Source: Stanley Baron's Brewed in America, an oldie but goldie from 1962.
To add to my other post:
In the wake of the Revolutionary War, Washington was a steady purchaser of primarily porters and a little ale, usually for entertaining. In the late 1780s and a little into his presidency, there are reports of Washington ordering bottles of porter by the gross, usually from brewers in Philadelphia. He was still placing orders through 1796.
The famous Washington small beer recipe comes from a notebook he kept while serving as a colonel in 1737, so I'm not immediately sure whether beer was brewed at Mount Vernon later.
Source: Brewed in America again.