As far as citterns, you might like this portrait of Dorothy Briggs playing one, now at Winterthur.. The article says it's an English guitar, but that's overly fussy. The English guitar was a kind of cittern that was popular circa 1770, both in England and somewhat in France. Like all citterns ( and like fretted duclimers) it tended to have special tunings that granted easier chords in a few keys, so an amateur could use one more easily for accompanying a song- and you would imagine that if Briggs had a good voice for singing, she would be quite a hit.

The 17th c. colonies were often a very hardscrabble affair, with little room for culture and music. Even 100 years later Thomas Jefferson would whine about how little good music was around, as he was smuggling a few instruments past the embargo on fancy imports during the Revolution. But Puritan antipathy to music is overstated. Certainly they had little use for instrumental music in church services, just as they had little use for gilt wood carving in their churches. It seemed to be a silly distraction from the serious business at hand. Charles Firth's book on Cromwell's army has a pleasant anecdote of some Roundhead soldiers tramping into an Anglican church service, hearing the organ playing, and starting to dance to it. Puritans also frowned on the idea of a professional, full-time musician. But Puritans would sing psalms in their churches, and had no problems with music in their leisure time ( what of it they could get, of course). When the economy got better and the fervor abated somewhat, plenty of musical instruments were imported into Boston and there was, even in 1716, a dancing school.

There's mention of both a violin and what's likely spare strings and a tuning hammer for a something like a spinet /virginal in a ship's inventory at Jamestown in 1609., so even with the high death rate from disease in the southern colonies, at least a few people early on were making an attempt. A rather old paper on music in colonial Virginia by Mary Goodwin shows quite a lot of instruments being imported, sold and played in the better-off 18th c., including wind, brass and strings. The Anthony Hay cabinet shop in Williamsburg was even offering harpsichords for sale: almost certainly importing the actions and building the cases themselves, but this did not stop the Colonial Williamsburg museum from setting up a shop on the Anthony Hay site dedicated to making musical instruments in the 1970's ( which was finally just absorbed into the Hay shop some years ago). It was the 18th c. south that also saw the introduction of the banjo from Africa. Even if the Africans who brought it were kidnapped and forced to work in very harsh conditions, they managed to keep playing music.

Daniels, B.C. (1991). "Did the puritans have fun? Leisure, recreation and the concept of pleasure in early new England". Journal of American Studies