I have an extra SSD that i want to play with. I want to set it up in such a fashion, that by swapping the older computer's HDD with the "Super"SSD, be able to run at the first boot, a live distro(or even a couple of them) with a desktop enviorment for live/temporary sessions, or for further installation by user. Its important to note that the OS has to be as hardware agnostic as possible,and be able to install on most of the PC, regardless of architecture or configuration of the hardware.

If the SSD is recognized by the setup routine, the installation process will be similar to the with the normal HDD.

I meant that there is no need for USB or CD installation after changing the part. Just swap and ready to go.

Depending on the Super SSD's size you should be able to install at least 2 distributions.
I'm not a fan of triple booting but it can be done.

As far as live/tmp sessions you should be able to select when signing into the distribution what type of session you would want and if you want it to be saved for future sessions. Setting up a Guest account would be an alternative to a regular user.

The Grub Menu will allow you to boot which ever distribution you want but generally Grub will give one of the distro's first boot priority unless you change that in the Grub configuration file.

You might also want to post the output of lspci to show what kind of hardware you have on this pc.
That way members could give you a better recommendation as to which distribution to install.
If this machine is being used for the enterprise or just home use and what you will be using it for.

-::-Giving details will help us to help you.-::-

The SSD is 250GB big. I connect to it via USB externally using Fedora Workstation. I don't know yet what hardware it will go on. I know its hard to answer to a vague question.

You could comfortably allocate 2 distributions to your SSD by creating 2 partitions of 124GB each and and create a swap of 1 GB.

Your vague answer is ok I get that you don't know what hardware it will be yet.
When you find out let us know-

If it's going to be ARM Processor Architecture I won't be much help. I don't have experience with that.

-::-You may want to try a Live Linux CD/DVD first to ensure that it works and see's the nic or ethernet card.

have an extra SSD that i want to play with. I want to set it up in such a fashion, that by swapping the older computer's HDD with the "Super"SSD, be able to run at the first boot, a live distro(or even a couple of them) with a desktop enviorment for live/temporary sessions, or for further installation by user. Its important to note that the OS has to be as hardware agnostic as possible,and be able to install on most of the PC, regardless of architecture or configuration of the hardware.

This is a bit unclear.

Install the live version of your distro of choice on the SSD. They are designed to run and install on most hardare. Debian has the most complete hardware support that I know of, including most ARM versions, PowerPC, and most everything else. Put the live Debian version on the SSD, and it should run on almost anything.

How to do that?

First download Debian and either put it on a usb memory stick that's formatted corretly or burn a live CD/DVD.

OK. Done

It took me about an hour to install Debian 8 "Jessie" and it ran great.