Hmm, so a bit of terminology to get you started: On Linux, there's the concept of "desktop environments", which is basically each a collection of programs to show you a graphical desktop UI. Basically, you can transform a server OS (which has only a terminal interface) into a desktop OS by installing a DE.
And there's various DEs available, which provide different user experiences. Among the most popular are:
- GNOME Shell (this is what Fedora and Tails ship with)
- KDE Plasma
- Xfce (this is what Whonix ships with)
- Cinnamon (this is what Linux Mint ships with)
- MATE
- Budgie
- LXQt
Now, GNOME has the best touchscreen support. KDE is in second place. The others don't really support touch input to my knowledge.
However, GNOME is also among the most heavyweight. KDE is definitely lighter, but also not the lightest.
I still think GNOME is lighter than Windows 8, so migrating will probably improve things, but if you've been told that Linux can revive old hardware, then yeah, your touchscreen requirement kind of torpedoes that...