Greg, I don't agree with some of the advice given here. So sorry for all your confusions when you are looking for guidance
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Since this is your first external flash, either 360 or 540FGZ will work fine for you. Once you get the flash, you should just shoot and experiment until you are comfortable with it.
The main difference between 360 and 540 is that 540 can swivel and is more powerful. But 360 is lighter and smaller and easier to carry around. So there is a trade off. My advice is that if you don't mind the extra weight and money, go for the 540. But if you do decide on the 360FGZ, it will work great as well.
The main advantage of external flash is bounce flash. I use one of the diffuser called StoFen Omnibounce; and it works great. Learn how to use bounce flash and your flash shot on your kids would look so much better than your built-in flash or P&S.
For macro, you should not need ring flash. Just use a reflector to redirect the light, or use wireless flash, which is easily accomplished using your K10D with either 360 and 540 (need to upgrade your K10D to firmware 1.10 or above, current firmware is 1.30). And wireless flash is also great for kids portraits, and it would make your flash shot very professional looking.
The Strobist web site is good, but only for manual flash and more advanced lighting technique. For your first external flash, I would stick with P-TTL, it is much more flexible. And I don't see the need for radio triggers, the built-in wireless flash works better in most of your needs (may only have problem in bright sunlight).