Great band! Seen 'em live, they put on a great show too!
Edges is my favorite by The Tea Party, but I like 'em all, frankly.
If you really like the feel of Edges, try out the band's debut, Splendor Solis. It's also very good.
Transmission is probably their heaviest in the direct sense of the word, a bit of electronic instrumentation also comes into play.
I see Triptych as a continuation of Transmission - a few more overtly commercial songs on there (which are good for what they are, though they've gotten overplayed a bit, at least in Canada), but still heavy, more electronic vibes as well.
After that, the band released a greatest hits album, Tangents, which is a fine overview and also has a few new songs on it, including a brilliant cover of the (admittedly, overcovered) Stones' "Paint it Black".
The Interzone Mantras, though, is probably the album which I'd recommend that you buy next. The electronic elements of the last 2 studio albums have been downplayed, and the exotic instrumentation heard on the first two albums isn't there to a great extent either - it's stripped down in that respect, but still very heavy, provocative music, and features some of the band's best (and darkest, IMO) songwriting. Definitely worth your hard-earned cash!
Yet to pick up the Alhambra EP though, so no comment on that.