For a normal bipolar transistor (not a darlington), Vce(sat) is typically quoted with Ib = 0.1 * Ic. Therefore, to achieve the value of Vce(sat) on the datasheet, you should plan the base current to be 1/10 of the collector current you want to switch. For example, if you are switching 60mA, design for a base current of 6mA. The base voltage will be around 0.7v and the voltage from the Arduino will be nearly 5V (assuming a 5V Arduino). Therefore a suitable base drive resistor would be around 4.3/0.006 = 717 ohms (nearest standard value 680 ohms).
If you are switching high currents, you should also bear in mind the 40mA current rating of the Arduino output pin. The highest current I switch with bipolar transistors is 500mA and I normally use a BC327 (PNP) or BC337 (NPN) transistor for switching currents up to this value. For these transistors, Vce(sat) is quoted at Ic=500mA, Ib=50mA. However, 50mA is too high for an Arduino pin. So I would design for Ib ~ 30mA and accept a slightly higher saturation voltage.
Above 500mA it is better to use a mosfet. Avoid using darlingtons, they have high saturation voltages so they get hot and need heatsinks.