I prefer the cover they did of Kate Bush's Running Up That Hill.
That's a great cover. I also really like their cover of the Pixies'
Where is My Mind.
Brian Molko has quite a nasal voice, so I suppose all their songs sound whiny if you look at it that way. You could try
Swallow, which has only spoken words, but if you want an song that's sung, maybe the ballad
My Sweet Prince. More upbeat options could be
Every You Every Me,
I Feel You and
Taste in Men.
I'm not a huge Placebo fan, but I have a few of their albums. Hope that helps!