I'll leave recommendation of classical harp music to others, as I have very few of these. A very good one is
Music of Alan Hovhaness: Concerto for Harp and String Orchestra: Spirit of Trees performered by harpist Yolanda Kondonassis. I like Hovhaness a lot: he is probably one of the most misunderstood composers of our time, his music often derided as "elevator music". Yet I think he remins true to his vision -- creating beauty out of simple means.
I'll turn to music of the folk harps, which I do own quite a few:
IRISH -- lots of good harpers here, I'll just name the top of the notch:
Patrick Ball is a practitioner of the brass stringed old Irish harp, and his series of four "Celtic Harp" recordings (under the label
Celestial Harmonies) are sparkling with grace and beauty. On these solo albums Ball performs various Irish, Welsh and Manx folk pieces, notably the works of the great Irish harper Turlough O'Carolan. I recommend starting with volume 3, which contains the best
Planxty Irwin there is.
Derek Bell, the late harper of the Chieftains, has an almost innate understanding of the music of O'Carolan -- he is the only one who can make any sense out of the last piece of O'Carolan,
Farewell to Music. His albums can be hard to come buy, but do make an effort to get at least
Carolan's Receipt and the live recording
A Celtic Evening with Derek Bell -- a wonderfully varied program, from Irish folk to new-age compositions and some rarely performed classical pieces. You've got to appreciate his irrelevant sense of humor during the concert!
SCOTTISH -- the prime suspect is William Jackson, and the easiest album to come by is
Inchcolm. The album features newly composed pieces, mostly in the traditional Scottish idiom. It showcases the Scottish "clarsach" harp in various settings -- solo, small ensemble, and with an orchestra. The final piece
A lover's Call is a very pleasant surprise.
WELSH Wales has a chromatic harp called the "Triple harp", and its greatest exponent is Robin Huw Bowen. Very interesting and uplifting music. The only album that is easy to find is
The Sweet Harp of My Land
Edit -- P.S.: do you say "harper" or "harpist"?