@katara asked me (or anyone) for recommendations on where to start with Prince. I’m not an expert, but I’ll throw in my two cents. The obvious starting point is Purple Rain, a monster of an album that should probably be in everybody’s collection. You’re already familiar with the title track and “When Doves Cry.” The rest of the album is just as good. Watch the movie too; “Darling Nikki” is even better when you see Prince slinking his way through that delicious filth.
After that, I think you could hit up 1999. It’s got a couple more hits (“1999” and “Little Red Corvette”), but I’d say the secret weapon here is “Delirious.” If you’re getting it on CD, try to avoid the initial pressings that omitted “DMSR” for timing purposes. Better yet, you could go all-in with the Super Deluxe edition.
More recently, I find myself picking up the posthumous “Originals” every time I’m in a record shop, but I haven’t actually purchased it yet. However, it does have his version of “Nothing Compares 2 U,” which I had dreamt of for years (I’ve found his live versions to be underwhelming, especially compared to Sinead O’Connor’s defining recording), and it completely lives up to my hopes for it.
I haven’t really heard any of his post-Artist Formerly Known As work, so hopefully someone else could chime in with more recommendations. I’ve heard that it holds up, but is less consistent.