I don't think you would ever need 10-12 inches if you have soil below the beds, unless you have specific climate issues. The main advantages of raised beds (1) the soil above ground will warm faster and get more warmth from the sun and (2) will be well drained. I have some beds that are 10-12 but they are on top of gravel, no soil below whatsoever.
We have a cold wet climate here but my Mom has raised beds made from 6 inch plank over ground that is pretty good, she can grow anything in those beds including tomatoes. The plank is not cedar, just the regular builder's plank (fir afaik) and without any treatment they stayed good for at least ten years - but that might vary depending on climate as well. That being said, we could probably do better with higher beds here just to get the ground warmer for tomatoes.
2 X 4 is enough to mark a bed, but I think 6 inches is about the minimum to really define a bed well so children and dogs don't run over it without noticing it is not the path. Also the weeds/grass or whatever you have there will quickly swallow up the marker that is only 2- 4 inch high. If you can do the 6-8 inch planks, you won't have to worry about building it up later.
