‘They found Mary, as usual, deep in the study of thorough bass and human nature’. – P&P. Ch.12.

‘Let their atttitude at the piano, or the harp, be easy and graceful…Similar beauty of postion may be seen in a lady’s management of a lute, a guitar, a mandolin or a lyre.’

-The Mirror of Graces (1811), pp.194-5 
Crosby & Co. London. 
(Republished by R.L Shep. 1997)

Many kinds of musical instruments such as the guitar, dulcimer, and flute could be found in Regency homes. However, the pianoforte and harp were considered most suitable for genteel young ladies.  JA’s heroines would be familiar with instruments like the violin, English horn, flute and three-stringed double-bass as they danced English country dances; the Boulanger is mentioned by JA in P&P. 
Various JA adaptations such as P&P2 and NA1 show scenes of an orchestra with stringed instruments. Musicians who played country dance music could range from a rustic trio to a chamber orchestra.

Patrick Piggot comments that in Jane Austen’s own music books was a volume of engraved music which contains a set of fourteen Sonatinas for the harpsichord or pianoforte, with an accompaniment for the violin, ad libitum, by Ignaz Playel. Playel was a famous composer of JA’s time.

Another volume of JA’s engraved music contains a flute obbligato* to some of the Songs in the volume.

*accompaniment as an essential part of the piece.

From JA’s music books, she was most familar with piano; the most common instrument of Regency ladies; Which may explain why JA’s heroines play piano.

My impression is young ladies at home may have played pianoforte or harp to accompany people playing on flute or violin. 

Emma Austen Leigh, a niece of JA kept a record of her Christmas gifts. Her 1813 ‘gift diary’ recorded from Papa- A Tamborine.

From The Ladies magazine, July 1801 picture and comment from ‘The Mirror of Graces’ (1811) it appears it wasn’t unknown for young ladies to pose with a guitar or play upon a stringed instrument in JA’s time. 
See link below.

https://pemberley.com/janeinfo/1801gtar.gif

References :

‘Bingley danced the two Second and the two Fifth 
Dances with Jane’ 
http://www.georgianindex.net/Dance/dance.html

‘That’s Entertainment’ 
http.faculty.rmwc.edu./janeausten/reports/entertainment.htm

P. Piggot. 
The Innocent Diversion. Music in the Life and Writings of Jane Austen. pp 143-144, p.146. 
(The Clover Hill Editions. London. 1979)

M. Hubert. Jane Austen’s Christmas. (Sutton Publishing 2003) p.81