Tom,
I didn't measure my own, but on searching I found that the arduino board consumes about 26 mA when powered by an external supply, 35 mA when using USB. But I was surprised to find the LCD board I have consumes 120 mA typically (150 max), and another 100 mA for the backlight.
The Meanwell should draw very little on it's 0-10v control input. So, you should be able to use that RadioShack 9V supply without any voltage regulator circuit for both the Arduino+LCD and the Meanwell control lines if it's capable of supplying at least 285 mA. But as mentioned, make sure you measure what voltage the PS is actually putting out unloaded.
If you want to bump up to 12v then you can supply the Arduino+LCD with the 12v, and use that 78L10 regulator just for the pot feeding the meanwell.
--adam