Home defense "for a woman" is your first mis conception.
It's all about the level and quality of training... and willingness to use that skill set. If she doesnt have the mental and moral perogative to shoot someone in self defense she probably doesnt need any gun around. In my opinion- anyone who stays with some "shoot to wound" or "rack the gun and they will run" attitude after a modicum of good defensive training (or even the minimal CCW training) just didnt "get it" and may be a bigger hazard to themselves than any gremlin they encounter.
"Women" can run any firearm a "man" can... and in some cases- better. Woman are not blessed with testosterone. If you have ever taught women to shoot you notice this right away- they are open to instruction and are not "hard wired" to shoot guns like guys are. Therefore- women tend to actually do what the coach says and tend to get pretty good results if taught how to do most "man skills" in a proper venue.
Learning.
Guide her to the adequate products. Present several for evaluation and let her pick what she wants.
That being said- my results have been better steering women to "man sized guns" like Glock 19's and M&P 9's. Much easier to shoot well compared to what the average gun shop clerk will steer her to--- usually a snub nosed revolver or some 380 ACP poodle popper.
Shotguns? A 20 works in the home enviroment as well as a 12 will. Be advised- ANY shotgun with a long length of pull or stock that doesnt fit right will hurt more than one that does... that goes for men as well as women.
Pumps? Sure- but she has to be willing to drill with the thing enough to run it under pressure. Like Dennis- I kinda like the idea of a short semi auto...for the reasons he mentioned already. If the stock fits she will be able to shoot a 12 as easily as a 20. If the 20 is what she likes or all you have.
Final note. In the last 6 months I've taught a legally blind woman, 5-1, 125 pounds to shoot defensive pistol. She showed up with a 25 ACP and a M9 Berratta. She dumped the M9 after 5 hours with a Glock 19. She's been shooting IDPA a couple of times a month--- and can hold her own on targets out to about 15 yards. Her sight limitations won't focus the end of a shotgun... and she finds them a little to big for her small size - the handgun is right up her alley.
We had the Berretta Tomcat out the other day... she fired a magazine from it. "That sucks", she said. Like most women, that cute little gun looks awesome till you get some skills going and find out it's not the A ticket compared to a bigger gun and a fighting cartridge. A few woman I've worked with carry 45 ACP pistols now days.... and some of those ladies prefer 1911 style guns with all those complicated safety levers on them.