Removing the old HDD was easy; one screw, pull and there you are. After that few more screws and SSD was ready for action. No need to enter the BIOS. SSD drive was automatically detected.
I'm fond of Raspbian (download here: https://www.raspberrypi.org/downloads/ ) which is based on Debian Linux. As it's available for PC the next thing to do was to burn Raspbian ISO on a USB stick. Installing Raspbian took less time than did with the original HDD.
So how is it? Well, I was afraid whether a modern a 3rd generation SSD would work on an old PC or not. SATA III is said to be downward compatible with SATA 1. One has to be careful and read what other userd have experienced. In my case X60s accepted the new SSD drive.
Now I have a very responsive old PC running a modern operating system. A new SSD is the best thing to do when you come across an old PC!
PS What happened to the old HDD? It has a new life as an external HDD!