Debian (I know) and Slack (I think) both offer network install options. If you know what you want to run and make wise package selections, that would work.
The easiest default choice is going to be something like Vector Linux. It will run (with GUI) on a system like yours by default. The install file can be copied to the hard disk and booted from floppy for install.
You could copy the install file to one hard disk and then temporarily connect to each computer in turn as a slave long enough to do the install
I usually run the Belarc Advisor
(if there is a running Windows system) to quickly find what hardware the computer has.
I do a quick hardware check with TuffTEST
, maybe a further memory check with Memtest
, check the hard drive with the manufactuerer's hard disk utility, and wipe the drive with Autoclave
Then I start from scratch and partition, format, install.
Watch out for boot sector virus' on the old PCs.