I'll probably get flamed for suggesting a "small" caliber handgun, but the Bersa/Firestorm (sold under both brand names) has a very nice little .380 compact that has minimal kick and fits a smaller hand nicely. Also, not too hard to rack the slide back. Comes with a nice price (mid 200's) -- please no cracks about saturday night specials.... Not to say that the 9mm Glock is not a good choice, either.
As far as shotguns go, the Mossberg 590 is, as far as I can tell, indestructable, but you have to ask yourself if you need to cough up that kind of money for a home defense weapon. The Remington 870 is a couple of hundred dollars cheaper, and probably more than adequate.
As far as edged weapons go, I'd suggest extensive training before you go that route. That's got to be anyone's last resort. Really.
A friend of mine who is a cop carries a .380 Browning in her purse. She claims it is the perfect gun for up close encounters, accurate, light, packs plenty of punch, 8 rounds, 9 if have the clip full and one in the pipe.