Tinjaw: I know this isn't the best/appropriate place to ask, but please forgive me as I want to get people to answer this that have read this guide.
I have never owned a "real" camera. I don't know how to use one. I have decided to buy the Panasonic Lumix DMC-LX7 as B&H had it for $299 (oddly the white versions was $449).
I am going to buy a book and some online courses to learn how to use it and take photos.
*My Question is* What low cost flash should I purchase that will work with this camera that will be good enough to use while learning? I have no idea what I need/should buy.
Get the Metz 24AF dedicated for Olympus/Panasonic. It's not expensive. Guide number 24 is just about the minimum for bouncing light off ceilings, and you gain the extra benefit of decent TTL metering. Bounce flash looks natural. It's also brilliant for close-ups of small things, using a couple of reflectors.You can of course use the flash straight ahead indoors for a bit more reach. External flashes of any description will save your camera's battery, too. A flash gun using AAs might drain those cells after 120 shots, although it varies a lot because the flash won't be firing at maximum power all the time. All you want is a touch of light, so it doesn't look like flash. Don't waste money on any flash that won't tilt. Large ones that both swivel sideways as well as tilt are better, and more power is better for bouncing, but they would be larger and considerably more expensive. Once you start using bounce flash you'll not want to be without it.