If I understand correctly, you're going to use this as a variable output voltage power supply, to supply various things, but also want to power the Arduino from it.
If so, RunawayPancake misunderstood your post. If not, I misunderstood your post.
And the Arduino will monitor the output voltage, among other things.
So the problem is how to derive a supply for the Arduino.
Since I assume that at times the output might be adjusted too low for the Arduino, and possibly even as low as 1.25V, (the absolute minimum that you can get out of this circuit), you will need another separate supply for the Arduino, taken from the rectifier before the LM350, then separately regulated to either about 8V as suggested by RunawayPancake, or 5V for a direct connection to the Arduino's 5V rail.
The best thing for this is possibly a small switching DC-DC converter module if the rectified DC voltage is 12V or higher, to keep power dissipation to a minimum. (You'll already have enough problems with dissipation, using a linear regulator for your power supply.)
You don't mention the transformer's voltage rating. Could you tell us that please?
And out of interest, what voltage and current range do you want from the power supply?
As mentioned, you might have some serious power dissipation problems, especially when the output voltage is low but the current is high.