Out of interest, how are you going to calibrate the sensor, the measurement circuits, the controller and the 4-20 output driver on your TDS measurement controller.
If you are not then why are you being so pedantic about 1 part in 10,000
If on the other hand you are going to make up or buy calibration samples and use alternative measuring devices such as DVMs then how are you ensuring that they themselves are accurate to 1 part in 10,000 (0.01%)
I trust by now you are seeing the point that I and several others are trying to make.
Unless you have calibrated standards that are directly traceable back to the national standards - which you won't have - then measurement MUST only be considered as a RELATIVE process. As long as you are confident that several measured samples relate to each other in a consistent manner then that is, to all intents and purposes, "good enough".
Working to 1, 10 or even 100 parts in 10,000 is, for applications and equipment such as you are using, impossible to achieve. What makes you believe the sensor, measurement and output systems are either accurate, linear or repeatable. And don't take the manufacturers word for it because at best they will only admit to a 1% total tolerance (100 parts in 10,000).
Individual errors accumulate so at best you might have a system that might be accurate to say 5%. But even that, if consistant, will be good enough for your application.
As to the "bouncing" of your arduino measurement, do the averaging equations as others have suggested. You might also want to fit a pair of capacitors, say 0.1 and 1000 microfarad across the 250ohm resistor. Voltage rating can be anything greater than say 12 volts. These will eliminate high and low frequency noise picked up from either the environment or the controller.