Wawa:
First of all, I assume you use an Uno or Nano.
The answers might be useless if you use an other Arduino.With a 250 ohm resistor, results depend on the stability of the 5volt supply.
That might be crap if you power the Uno from USB.250ohm also means danger for the Arduino if the sensor outputs more than 20mA.
Much better to use a 51 ohm resistor (standard 1% E24), together with the internal 1.1volt reference.
See the diagram in this thread.You didn't say what the temp range of the sensor is.
Note that you only have about 800 steps of you measure 4-20mA sensors with Arduino's 10-bit A/D.
If that's not enough, then you might have to move up to an ADS1115 breakout board.
Same circuit can be used, but resistor value must be adapted to the ADS.
Leo..
I like your proposal Wawa...but it is really necessary use a low pass filter? what signal am i filtering with Fc = 1.6KHz in this case?