I think an important thing to do is to avoid talking to, or within earshot of, your daughters about problems that you see as being disturbingly common in females. They may develop the idea that they are EXPECTED to struggle with these issues.
Example: My mom was concerned about Female Math Anxiety. She and her friends did a lot of fretting, within my hearing, about how terrible a handicap so many girls have "because schools and society teach them that math is scary and difficult." My mom complained to me directly that she had had trouble w/math since puberty, that she expected to be bad at it even before she had tried, and that she avoided math in her adult life. (She never said HOW she got this way, though.) I found math classes unperturbably easy until we got to multiplication; then, when I didn't comprehend it after the FIRST lesson, I thought, "This must be Female Math Anxiety! The school is making this difficult for me because I'm a girl! I'll never be able to learn this!" and I stopped paying attention. When my parents and teacher spoke to me about it, I argued that I was going to be a librarian when I grew up and librarians don't need to know math; my parents quickly came up with an example where a librarian would need to multiply, which made me furious and despondent because I felt they were telling me that my Female Math Anxiety would make it impossible for me to get any kind of job. I was then forced to listen to a record of sing-songed multiplication tables every morning while my mom yanked the tangles out of my hair.
: I did learn them, but the annoyance and literal pain associated w/the process deepened my bad feelings about math. It was not until trig (when I had a really great teacher, who not coincidentally was ultra-feminine) that I stopped reacting to the slightest difficulty with a new math concept by panicking and refusing to pay any attention at all to it. I did not do this in any other subject area. I really believed that, as a female, I was entitled and expected to panic at math, that the culture was somehow forcing me to react this way and it was out of my control.
Several women have told me that they had the same feeling about eating disorders: It was not that their female role models actually HAD eating disorders, but that their mothers or teachers or the media were fretting so much about how "girls today are so obsessed with their weight" that they felt it would be ABNORMAL to have healthy eating habits and maintain a normal weight!
is just to say that I think it's important not to overemphasize the scary things that can happen to girls and women--especially, not to label as female issues things that actually can affect both sexes.
As for mainstream teen magazines, I think it's important not to ban them. Instead, take a look at them from time to time and use them to start discussions: "I was amazed that they found 14 pages of things to say about eye shadow! Did you think it was interesting?"
Rather than "dates" with Daddy, I'd go for regular spontaneous conversations in which Daddy shows genuine interest in whatever the girls are into--even if it's eye shadow, he can ask them to explain the techniques, etc. If you want to schedule 1:1 time w/Dad (or Mom) to make sure each kid gets enough attention, make the focus something that that kid really enjoys, not necessarily a "special occasion" kind of thing.
I guess my overall feeling is that the best way to raise strong women is to concentrate on raising strong (and kind and gentle!) PEOPLE and not think about gender issues much.