You are insanely lucky that she sent you that track in particular, that is probably one of my favourite five songs of theirs, and definitely my favourite from VLV.
You're right that he doesn't stay in the lower register to quite the degree he does in Yes on too much of their output. If that's an aspect of Coldplay you enjoy, if I could suggest one track, it'd probably be Politik, the opening track of Rush of Blood to the Head. Or the title track.
Or just check out that whole album. VLV was the album that brought the band far greater respect amongst more "discerning" rock fans, and thus there's a huge base of people who would tell you to just start listening there. But from what I've seen, in the eyes of many older Coldplay fans, Rush of Blood is still their magnum opus. You couldn't go wrong starting with either though.
I'd avoid X&Y like the plague. It's not without its merits, but its by far my least favourite album of theirs because he spends far too much time just riding on that broken falsetto. So I can imagine if you like his lower singing, it's not likely gonna tickle you the right way.
Their latest is also great. I personally probably prefer it to VLV.