Transistor help please

slipstick:
Have you ever seen a published circuit with a TIP120 connected to an Arduino without a base resistor?

Yes.
Unfortunately in an official tutorial ON THIS SITE.
Same long-standing mistake as the capacitor in the shift register tutorial.

A 1k base resistor for a TIP120 darlington is OK for collector currents up to about 1Amp
For higher collector currents (up to 4Amp), you can drop that to 220ohm (so 470ohm for ~2Amp).
The TIP120 gets hot >= 1Amp collector current, so needs a heatsink.
Better to switch to a logic level mosfet, especially for collector currents > 1Amp.
Leo..