Re: Kokikai v. Aikikai
I have not gotten to train with Kokikai but have observed a class or two. They look superficially like Ki Society, but of course I haven't had a chance to learn about subtle differences.
The biggest differences you'd see in joining a Ki Society dojo from Aikikai would be narrower stance, lighter footwork, softer technique, some throws de-emphasized or prohibited, and use of "ki tests" to assess stability and relaxation. My understanding is that additionally Kokikai, even more than Ki Society, de-emphasizes breakfalls and teaches only techniques from which uke can successfully roll.
I know several people who have gone in the Aikikai-Ki Society direction. It can be frustrating at first as you're repeatedly told to stop using approaches that have worked for you in the past, but it gets better with practice, and I'm told that the contrast is quite interesting. (It has been for me, going in the other direction.) Kokikai is a reputable style of aikido and if that's the convenient dojo for you I don't see why you shouldn't try it out. As always, observing or trying a few classes is a good strategy.