I'd say start with TDS or The Fragile. Most fans regard them as two of NIN's absolute best works. Of the two, TDS is a bit more accessible, but if you're in the mood for a musical journey that's going to take you everywhere and back, The Fragile is your best bet.
With Teeth is probably their most commercial album, and while half the songs are good (The Hand That Feeds, Right Where It Belongs, the underrated Sunspots), the other half are mediocre at best.
Year Zero really divides fans. Personally, it's my favorite NIN album, but to my best friend who got me into NIN in the first place, Year Zero was the final nail in the coffin for her idolizing Reznor. With that said, I still give it three enthusiastic thumbs up.
The Slip is like With Teeth, in that half I like, half I hate. All I have to say.
Regarding Pretty Hate Machine, it easily sounds less like NIN than anything else, due to being so spectacularly 80's. Going from PHM to TDS would be like WDADU to I&W, times two. Though it has some great songs, you can find heavier, more energetic versions of most of them on the live CD/DVD And All That Could Have Been, or even Beside You In Time.
Broken is kind've like PHM, in that all the best songs on there have better live versions elsewhere, plus it's so damn short. Ghosts is good, but it's not really representative of what Nails is about as a whole.
Anyway, just my thoughts. Hope that helps. I'll be seeing them on the 29th, so I'm thinking that'll probably rekindle my NIN love.