Agree with most of what has been said already. Lots of good choices. Enya and her producer did come up with a pretty solid and mostly unique sound on those first albums. I don't have an extensive collection by any measure, but I do really like Watermark. I actually have it on both German and US vinyl and it does sound very good. Not great, but still very good.
The Hector Zazou disc I've mentioned around here before called Lights In The Dark does have some of that same old world Celtic flavor, albeit with some tasteful instrumentation, usually in the background. Very spiritual and haunting recording. He resurrected some ancient Celtic songs and refreshed them with some modern music production employing the vocals of three very special ladies, along with his usual cast of luminaries including Brendan Perry of Dead Can Dance. Beautiful sound too. Maybe too religious for some, but very beautiful nonetheless. Just checked and there are places where you can listen to it online. Some comments in the links below ...
http://db.audioasylum.com/cgi/m.mpl?forum=music&n=15603
http://ectoguide.org/artists/zazou.hector#lights
That first self-titled recording by Anuna from the late 90s has some beautiful voices as well, mostly a capella and recorded very simply in a church. Might wanna listen to some samples of that and see if it connects with you. Nothing really as dramatic as that Lisa Gerrard song that I can recall right now, but one of the ladies, Katie McMahon, is on the Hector Zazou disc too. Kind of lite in a Clannad and Enya way, but nice.
But one I'd definitely check out is Seattle's own Heather Duby. Try to listen to some samples from Come Across the River, or read the AMG review. Very nice voice. Here's what amazon said about her first one ...
Amazon.com
Sub Pop Records in Seattle was the originator of grunge rock; in the years since Nirvana's rise, the label has focused on diversifying with topnotch talent in all fields. Producer Steve Fisk has emerged as a secret weapon, collaborating with artists to ensure that their sound is unique yet not overwhelmed by intrusive arrangements. Heather Duby is a Portland native who moved to Seattle to work with acts such as Evil Tambourines and Maktub. Duby established a relationship with Fisk, trading tapes and working out the schematics of what's become this texturally rich, subliminally somber song cycle. British singer Beth Orton has beaten everyone to the punch commercially, lining folk tunes with trip-hop beats, but while Duby works in similar fashion, the outcome is closely hewed to the 4AD label's line of gothic psychedelia. The tunes work together to form a feeling not unlike that of traipsing through an old, drafty Victorian house with the black lights and lava lamps on overdrive. --Rob O'Connor
