Yeah, the 0 and 1 pins will have some noise on the Arduino. Those pins are the default pins used for Serial.print messages as well as programming the device I believe.
You can create a software uart on any other 2 pins and use that instead. Should look something like this:
SoftwareSerial mySerial(2, 3); // RX, TX
Note that according to the Arduino docs:
If using multiple software serial ports, only one can receive data at a time