I'll chime in, but I'm kind of a "mixed drink"... more jujutsu than anything else.. but I do love the work...
Like you said, there are a number of kata out there, but really only one that seems to be pretty standard in all the schools and seminars I've visited. Almost any Aikido school can teach it to you in a few classes. I don't have it on video and wouldn't attempt to try to talk you through it, but I will give you some advice.
First of all, don't "twirl" the jo like a baton... it's a weapon. It's meant to be used to strike and punch. It is a method to extend ki, and your technique should be the same with or without the jo (or bokken).
Second, work the weapon on your body centerline or aligned with your hip, depending on the technique... thrusts should be done like shooting hard with a pool que.
Third, every strike has a specific target. Don't just swing the jo in the air, but at imaginary target areas of an opponent. A small or medium sized tree makes a good "hitting opponent" target to use as a makiwara.
My last instruction would be to keep your elbows in their natural position as much as possible, and use the natural flow of the weapon to guide the ki extension as much as possible. While having a kata is good, simply having good "sword technique" with it will make it workable as well, and you can follow whichever kata lead you want as a standard.
Remember true martial arts are based on intent, so be deadly serious when using or facing a weapon. It will make all the difference in how well you use it, and what it brings to the table from its use.