Red makes you sexy, dumb, attractive and repellant sums up a lot of research on how red is perceived when it's worn by women. Yes, it makes you more attractive in others' eyes, but it also can signal that you're interested in sex, or stress out your observers. There are positive and negative perceptions that have been measured, most of which aren't (I'm guessing) how you want to be seen or the impact you want to have on your audience.
But I've got them beat with a reason to reconsider red: Especially on camera--whether for a web video or television--red looks like it's "bleeding" or disintegrating around the edges. That's true whether you're wearing a red jacket or red lipstick. Opt for a saturated but less vibrant color close to your face, and a dark jacket for a crisp look on camera. If you have light hair or white hair, a dark jacket will give you a better frame as well.
Looking for famous speeches by women? Check out The Eloquent Woman Index of Famous Women's Speeches, with a wide variety of women speakers, types of speeches and topics to inspire your next speech. Each one comes with lessons for speakers, plus video or audio and a transcript, where available.