That seems like a very old computer. Congratulations for the considerate
spirit of anti-consumerism. I don't think that much modern graphical software
is developed targeting systems with a small RAM capacity such as 12 MB (or
MiB). Running old software is also problematic because it's unmaintained, so
you would be on your own for the problems you may find if you used versions
of the software contemporary to your computer.
I suggest that you ask for suggestions in the X11 mailing lists; they may
help you to tune a graphical setup to minimize resource usage. You can also
run a modern environment with a console setup; any general purpose GNU/Linux
distribution can do that, such as Trisquel. Some GNU/Linux distributions
target small systems, such as the FSF-approved LibreCMC and LibreWRT (I
haven't used them); maybe you can use them or ask in their communication
channels for recommendations. They're likely to know about how to run on
limited hardware.
However, I think that the issue is mainly about which software packages you
install and how they're configured, rather than which distribution you use.
Bear in mind that some software compiled for x86 may need instructions not
present on your computer. That software will crash in your computer (The CPU
interrupts the kernel for an invalid exception and the kernel terminates the
program. I don' know what would happen if the kernel attempts to execute an
invalid instruction, however). If so, you will need to re-compile that
software.
I think that computers have been getting more energy efficient since their
appeared. For doing intensive computation (Such as compiling a large
program), it will be more energy efficient to do so in a modern computer than
the old compute you're talking about. I mention this because you're concerned
about wasting.
Instead of installing from a floppy disk you can try booting from the hard
disk. Bear in mind that initiating but not finishing an installation may make
your system unbootable, so you may end using a floppy disk anyway. I wrote a
message where I gave pointers about how to install from the hard disk, but I
can't find it. I pointed to the manual of installing Debian (Trisquel is
indirectly based on Debian). See
<https://www.debian.org/releases/stable/amd64/index.html> and search for
“hard disk”.
