My first reaction after listening to this portion of the podcast was that of either one or both things. My first thought was a katana, or if you would rather a shorter straighter version, what has been modernly referred to as the ninja-to. Since my fondness of Japanese culture and history I would prefer either a katana or wakizashi. To be honest, though, the use of both at the same time would require a lot of room. Thus, a shorter sword such as the ninja-to or the wakizashi would be preferable, for me, in home defense in absence of a gun. If you use a tanto you might as well use any other fighting knife out there. If such were the case I would suggest a ka-bar.
Reason for use of a wakizashi over a samurai sword deal mostly with the arc of a swing necessary to use it effectively. Samurai swords are longer, and are not well used in hallways and near doors. The wakizashi is long enough to keep your opponent away from your immediate area, and it still has the bite of a samurai sword, in my humble opinion. You have to realize that these swords were meant for slicing, not chopping, or hacking. Thus, they are lethal if used to attack the corresponding places on the human body which would lead them to bleed out quickly. Its not like the films where you slice off an appendage. Realistically some wounds that did not look bad prooved to be fatal due to severed arteries.
I would not want to face someone who had a gun and I only had this to defend myself but it would be the first thing I would use if such were the case. If you wanted to be non-lethal about it I suppose you could use a bokken (which is essentially a wooden samurai sword of equal weight). The sword's master, Musashi, used a bokken he had fashioned from an oar to win his first match. His opponent didn't survive.
If you are looking for a ranged attack I would suggest a good bow and arrow. However, if they are that far away from you I would think you would have enough time to call 911.
You could use other swords, but many were made to be heavy enough to cut through armor and such. In effect they are cumbersome in home defense.
The only other weapon I would suggest, if you could learn how to use them, are Sai. These are highly effective for both defense against an attacker who does not have a gun, and for attacking said aggressor. They can be used with pressure points to incapacitate them, or give them sufficient blows to where they will stop attacking you. They are not as lethal so accidentally killing your assailant is not as likely unless that is what you are intending to do.
So the short of my long dissertation is either a wakizashi or a pair of sai.
