Celtic music is one of my favourite genres, but one needs to tread carefully here. Originally, it was meant to define the folk music of Ireland, and by extension, similar styles from England, Scotland and Wales. However, there are a lot of CD compilations these days that have 'Celtic' as part of their titles, but which deal with pop, easy listening tunes and New Age.
Case in point: Clannad. They started out a pure Irish folk group, singing in Gaelic and English, with authentic folk instrumentation. Along the way, they switched to synthesizers and transformed into a pure pop sound , with New Age dimensions. Led by the two Brennan sisters Eithne (pronounced Enya) and Maire (pronounced Moya), both of whom have now become pure New Age artists, Enya especially. This is music to demo high-end audio.
Loreena Mckennitt is a superb Celtic artist, composing, singing, playing harp, arranging and producing her CDs (all of which I admit to owning), but she too skirts dangerously close to New Age. Only her intelligence and musical sophistication sets her apart from the crowd.
If you wish to explore the genre, both in terms of instrumental music, and of singers in the folk and folk-rock mode (Irish mainly), you could check out:
The Chieftains
The Dubliners
De Danaan
Clannad (early albums)
Planxty
Moving Hearts
The Bothy Band
The Pogues
Christy Moore
Niamh Parsons
Susan McKeown
Dolores Keane
Solas
With instrumental music, the slow airs can be beautiful, but any CD filled with jigs and reels is best avoided. This is folk dancing music, which may sound better 'live' but can be a bit too high-pitched and unrelenting on record.
The related genre to Celtic is British folk and folk-rock, with major artists such as:
Fairport Convention
Steeleye Span
Pentangle
Bert Jansch
John Renbourn
Capercaillie
Battlefield Band
June Tabor
Martin Simpson
Martin Carthy
The Watersons
The Imagined Village
Kate Rusby
Oysterband
Sandy Denny
Malicorne (Breton folk)
Alan Stivell (Breton folk)
Plenty more, but these are the ones that may be easier to find.