Basic Discography (I'm leaving out the EPs and what not):
Warlock:
* Burning the Witches (1984) - an excellent debut; If you like the heavier, thrashier stuff, than I highly recommend this
* Hellbound (1985)
* True As Steel (1986)
* Triumph And Agony (1987) - best of their albums IMO
* Earth Shaker Rock (1998) - Compilation, this includes a few "Doro" songs, but is mostly Warlock material
Of the Warlock stuff, I recommend Triumph and Agony for a first time listener. It's the album that hooked me on Doro from the first three notes. Earthshaker Rock is also a very good "best of" compilation.
Doro:
* Force Majeure (1989) - probably the heaviest of Doro's early solo albums; includes a cool cover of "A Whiter Shade of Pale"
* Doro (1990) - produced by KISS bassist Gene Simmons, a pretty solid album with a fair mixture or hard rock and ballads
* Rare Diamonds (1991) - Compilation, mostly Warlock era with some solo Doro
* True At Heart (1991) - mostly ballads from what I remember, not what I'd consider one of her better albums IMO but I do prefer her heavier stuff
* Angels Never Die (1993) - lots of ballads on this one too, but Bad Blood is an awesome song (cool video too)
*
Doro Live (1993) - excellent live album!
* Machine II Machine (1995) - more industrial style metal, heavy crunchy and somewhat electronic sounding, but still a great album
*
Love Me In Black (1998) - available only as German import, includes some of my favorite Doro songs (title track, Brutal and Effective, Do You Like It?), also more on the industrial/dance side of things, but still really heavy; includes an awesome cover of Heart's Barracuda
* The Ballads (1998) - all ballads Compilation
*
Calling The Wild (2000) - One of my favorite Doro solo album, completely solid album IMO, great cover of White Wedding, guest appearances by Lemmy on two tracks, highly recommended
*
Fight (2002) - a dark and heavy album, includes quest appearance Peter Steele on one track
* Classic Diamonds (2004) - a compilation of Warlock and Doro hits rerecorded with a full orchestra, pretty cool stuff, but I don't know if I recommend it as a first listen
*
Warrior Soul (2006) - excellent and very solid album, was one of my top albums for that year, highly recommended
* Fear No Evil (2009) - overall not as good as Warrior Soul IMO, but still has a good amount of kick ass tracks
I suggest starting with the ones in bold, but those are just the ones I think are the best.
That was probably more than you needed, but hey ... I could have done all the DVDs and singles too.

Let me know if you have any other specific questions.