Holy Priests are the only priest spec that focus on healing, disc and shadow are both DPS but still have nice self-heals. Holy priests are pretty strictly heals, though, and they only have a few (3?) damaging spells. Disc and shadow are both pretty solid DPS but I've never capped a priest so I'm not a good source for that info. I do notice a lot more disc priests in BGs and arenas, at least in my experience. I couldn't tell you what the advantages and disadvantages are of the specs however.

A priest's role in a raid is whatever their spec is. As a shadow or disc priest you shouldn't be healing anyone in the raid except yourself really. And as I said earlier you're pretty much useless damage-wise with holy, but they make up for that in hella great heals.

Fantasy-wise priests are really cool. Holy priests are the servants of the Light who use holy power to heal their allies. Shadow priests really go against everything that holy priests are about -- they're all about destruction and driving their enemies to madness to defeat them. Disc priests are cool because they're the "balanced" spec that sees power in both the Light and the darkness and uses strict discipline to empower themselves and tear their enemies down. Priests are one of the most quintessential classes in WoW and certainly the most thought-of healers, but that's definitely not their only power.

All this being said, if you aren't looking to heal then you should definitely dual spec shadow and disc, play around with them for a while and get a feel for which one fits you best. If you're interested in healing then priest is a good place to start, but you could still dual spec a DPS spec if you wanna try that out too. The last time I played a priest was WotLK and i only got it to 60-65 so my info is pretty subjective. I've always liked shadow priests because they get the cool shadow presence thing that makes them look badass.