Parachutes' songs are all really simple, which could be a drawback for you, depending on your personal taste, but their simplicity invites dozens of interpretations for each song, and I like the overall sound (ie acoustic guitars and what-have-you) of it better than the other albums. The songs are more unified sonically and I just think they are in general more "artful" than most of the other Coldplay songs.
X&Y is my next favorite album right now for some reason, though, and it's almost the polar opposite of Parachutes, and I don't really know why that is. I guess I like the synthesizers almost as much as the acoustics. And X&Y-era songs are more lyrically complicated than AROBTTH songs or VLV songs. imo.
And AROBTTH is a good album; I absolutely love about half of the songs, but the rest are slightly more meh for me. So I suppose it's my third favorite, although it's close to X&Y.
Viva la Vida or Death And All His Friends is just terrible, I don't like Eno's footprint stamped all over it, and while the songs are pleasant to listen to I don't think they are as emotionally appealing to me for some reason. Although, again, I adore at least a few of the songs off of Viva La Vida, and I think Prospekt's March is very good, too, except they put in an almost unaltered-save-for-Jay-Z-rapping-over-40-seconds-of-the-original-song Lost+ and another very nearly unaltered Osaka Sun Mix, as well.
So that's my semi-comprehensive review of Coldplay.