Do you start fine tuning the system with cables or tubes ?

But how do you usually proceed ?

1st tubes, 2nd cables.

Learning the effects of tubes and cables usually requires hands on listening and subjective preferences. 

@faustuss depends on a component. Some run tubes harder and even the small signal tubes will wear out in 2 years. In process they gradually get worse. Power tubes only last about 1000-2000 hours. When they fail they can take out other parts and render the component useless. 
But yes typically with good components using the manufacturer recommended tubes might keep you out of trouble. I’m not anti tubes. I just know I’m done with tube gear for time being. And dumping money into tubes with today’s prices, you are more likely to get better ROI out of component upgrade. 

 Better NOS vintage signal tubes should last 5000 hours or more, especially from 1950s and military/industrial grade. Some vintage power tubes can also last for thousands of hours. Problem is availability of some of them from reputable sources.

But tube equipment, especially power amps, is for those who want to be involved. Like high end tape decks and turntables. Reward, besides the involvement , is great sound.

"Better NOS vintage signal tubes should last 5000 hours or more, especially from 1950s and military/industrial grade. Some vintage power tubes can also last for thousands of hours."

This depends upon the unit/design the tubes are being used in...

Certain designs from popular manufacturers are known "tube eaters" (CJ, AI & AR come to mind, but there are others as well - like Cary/Carey? and SF).

DeKay

DeKay, of course.