King Krypton, I think you were right in considering
BATMAN:STRANGE APPARITIONS to offer her.

It's the classic Batman series, a great sampling of typical superhero fare, and Englehart & Rogers provide a story with exceptional art, characterization and wild twists, while also being very true to Batman from his earliest Bob Kane origins.
Plus the stories are 17 pages each, a bit shorter than the newer stories, less per chapter for her to get through, and still outstandingly good.
I think it's a perfect choice, to show the intelligence, sophistication, fun and the art that can be realized within the parameters of a standard superhero story.



Other choices:


Millennium Edition: reprint of DETECTIVE 395
( Plus other Millenium Edition reprints of undisputed classics. )
This is one of my favorite Batman stories, and the first Dennis O'Neil/Neal Adams/Dick Giordano collaboration, beginning their classic run in DETECTIVE, and then later BATMAN also.




Wein/Wrightson SWAMP THING 1-10 (recently re-released in the 2nd edition of the SWAMP THING: DARK GENESIS trade)
The Wein/Wrightson run has a magic to it that makes me prefer these, even over the later Moore/Bissette/Tottleben run.
And the Alan Moore run would be a great follow-up to the Wein/Wrightson trade, to show what a huge change in approach can occur with a new creative team.





MANHUNTER collected edition, of the classic award-winning Goodwin/Simonson series. Another classic series, and all but the last chapter are in short fast-paced 8-page segments, which might make it one she'll more eagerly read.





CEREBUS, volume 1 (collecting the first 25 issues). This not only allows her to get in on CEREBUS from the beginning, but in this earliest volume, it's divided into 1-issue, 2-issue and 3-issue stories. Complete stories, but which are expanded on in the HIGH SOCIETY (vol 2) and later volumes of the series.

A great series that is intelligent, sophisticated, wildly funny and (something you expressed she has a preference for) not a series focused on violence.
CEREBUS is also a humorous commentary on many of the best comics series done over the last 30 years or so, beginning with a parody of the Roy Thomas/Barry Smith CONAN, Red Sonja, Elric, Bran Mac Morn, Englehart/Rogers Batman, Prince Valiant, Claremont and the X-MEN, Captain America, Neal Adams' Deadman, and the Marvel/DC competition over Swamp Thing and Man-Thing.
And CEREBUS parodies many other political, TV and movie personalities, like Groucho Marx, Nixon, Carter, Sgt. Schultz from the Hogan's Heroes TV series, Foghorn Leghorn and others.
It's a series where she can read and enjoy some of what she's already familiar with in popular culture, and that she can go back and re-read later with even greater appreciation, once she's read the other comics series these CEREBUS stories parody.





Another favorite of mine that has mind-blowing art coupled with good storytelling is BERNI WRIGHTSON: MASTER OF THE MACABRE 1-3 (1983, Pacific). Again, stories that are very engaging, and also short enough that she'll get through them and not lose interest. With a wide range of shorter stories in a single book.
For my money, these are some of the most ornately detailed pages of art in comics history. And possibly the best colored stories in comics history as well (colored by Steve Oliff).




Anthologies such as HOUSE OF MYSTERY might give her a good selection within one book too.
Vertigo's recent WELCOME BACK TO HOUSE OF MYSTERY reprint collection (1998) offers a wonderful collection of stories from the 1970-1974 period, with nice offset printing, of stories by Neal Adams, Berni Wrightson, Alex Nino, Jim Aparo, Bill Draut, Gil Kane, Wally Wood, and with a new Neil Gaiman/Sergio Aragones introduction and framing sequence.



Or EPIC ILLUSTRATED.
EPIC remains one of the finest anthologies in comics history, and one of the finest representations of the comics industry period.






A series I love that I shared with a past girlfriend is KAMANDI, by Jack Kirby.

Of all the things I gave her, this is the one thing she fell in love with and couldn't get enough of. Over time, she constantly asked me if I had more KAMANDI issues for her to read, and she read all 40 issues by Kirby.
She didn't like NEW GODS or THE DEMON or any other Kirby stuff I showed her, but she loved KAMANDI. I bought extra copies of a whole bunch, so she didn't have to return them and could re-read them, which I think she did often. Her love for KAMANDI outlasted our two-year relationship.




Another girlfriend of mine (from the Phillipines) really enjoyed the MARVEL CLASSICS # 2 : H.G.WELLS' THE TIME MACHINE, illustrated by Alex Nino.

She was indifferent to everything else, but re-read this one several times.







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"This Man, This Wonder Boy..."