I think there is a lot of Celtic music out there for classical and fingerstyle guitar now and at all different levels.
A first source that comes to mind is this website. There are some great arrangements of Celtic tunes under the 'our scores' section. For example, Nicola Conata has provided really nice and accessible arrangements of Mairi Bhan Og (an old Scottish song) and also of O'Carolan's Draught by the Irish harpist Turlough O'Carolan. A recording of each arrangement being played is also available on the website. There are also great arrangements of Wild Mountain Thyme, Star of the County Down, Blind Mary, the Rights of Man and a lot of other traditional songs. There is also a nice, really catchy arrangement of Brian Boru's March in the section of this website (towards the bottom of the home page) which provides free arrangements graded at different levels (I think it is in D03).
Some other sources that come to mind, include Keith Murray's website, which has arrangements of a number of Scottish songs available for purchase. Gordon Gibson provides a lot of free arrangements through the free scores website. Patrick Steinbach provides a number of arrangements for free on his webpage and he also has a number of books for purchase.
In terms of pieces that are now part of classical guitar repertoire, Turlough O'Carolan's music comes to mind. When I have heard Celtic music being played at CG concerts, it nearly always includes a piece by O'Carolan. I have seen that Melbay has a book (which you can purchase as a pdf with a recording) of CG arrangements of quite a number of O'Carolan pieces.