"What would you suggest as the ideal weapon for self defense, chez adult female who can handle everything in the study?"
The primary considerations as I see them would be (1) what the individual is most familiar/competent with, (2) what the individual can store responsibly and access quickly in her particular situation, (3) effectiveness, and (4) likelihood of overpenetration. So the ideal choice may differ by individual and setting.
At least anecdotally, it seems that if a self-defense shooting is clearly justifiable by the facts of the case, the model or styling of the weapon used will generally not come into play (assuming the weapon was a legally possessed Title 1 firearm). I am under the impression that weapon choice would generally come into play only if the case were questionable to start with. Weapon choice could play a bigger role in civil suits, though.
"(W)hat are your thoughts on juror perceptions of gender and type of firearm? Do you believe it matters?"
As one who does keep a firearm for defensive purposes, I personally weight projected juror perceptions well below familiarity, access, effectiveness, and overpenetration concerns. In the unlikely event that one needs to use a weapon to protect oneself from death or serious harm, obviously a successful outcome is of primary importance.
"With the scenario of (1) entirely innocent home dweller and (2) intruder a stranger planning to rob, steal, or worse...what factors do you think would aggravate the shooter's case, providing the DA would file?"
Again, I am not a lawyer, but it is my layperson's opinion that the choice of any practical NFA Title 1 firearm (whether handgun, rifle, or shotgun) would be much less important than things like the homeowner's demeanor, aggressive posturing prior to the incident ("trespassers will be shot" signs, that sort of thing), intoxication, and whether the homeowner was engaged in illegal activities at the time. I would expect that factors undermining the components of justifiability, i.e. imminent jeopardy and the mantle of innocence, would take precedence over the aesthetics of the firearm itself.
Where weapon choice can become more of a factor is in a civil case, particularly if an attempt is made to portray the shooting as a negligent discharge rather than intentional self-defense (which, as I understand it, would allow financial recovery from the homeowner's insurance). Demonstrated competence prior to the incident, and intelligent weapon choice (i.e., no hair triggers) can reduce the likelihood of such a claim.