What changes nixie tube displays?

"but is it worth the time?"
I enjoy it.

"how much time does it take to learn how to use arduino stuff? "
Depends how much time you put into it.
A minimal 16 MHz circuit only needs a 4.5-5V source, a crystal or resonator, a couple of caps and a 10K resistor. And whatever you decide to use for a socket, or connectors.
Then its just programming to make it do things.
Here's a simple program to make an LED blink. Everything is an expansion on something like this.

// declare variable names, or assign names to pins to be used
byte outputPin = 4;  
// define stuff that will happen once in setup()
void setup() {
// setup the pin to be an output pin (vs input)
pinMode (outputPin, OUTPUT);
}
// now write the stuff that will occur over & over
void loop() {
// set the pin High - in this case the pin is connected to the anode of an LED, cathode to a resistor, to Ground - so High is on
  digitalWrite (outputPin, HIGH);  
// wait 100mS
  delay (100);
// set the pin Low - turns the LED off
  digitalWrite (outputPin, LOW);
// wait 900mS - so overall the LED appears to flash once a second
  delay (900);
}  // end of loop() - go back & run the loop() code again.

Nixie tubes have multiple elements, one for each digit. To change the digit that is on, a different element is driven. Pretty straightforward.
The tricky thing is the voltage - they run at very low current, but at a high voltage - like 170-200V.
A special chip that can switch the high voltage on/off is used. Or a bunch of discrete transistors can be used instead.