Linux was designed for a 386. I think a P1 can handle it. The question is how many bells and whistles can you run in addition to the kernel.
Go here to see distros that are designed to run on computers that old. You'll notice i586 (Pentium I) is selected, so try 486 and even 386 for distros that will definitely run on your system.
Watch out, many older systems won't boot from CD.
“designed for a 386.” Hence the designation x86.
99% of all OS’s were. Again P1 is too old. I recommend SUSE Linux, my personal favorite. I have a P1 too. I keep it as a memento. It has caldera v1.2 I think. (All command line.)It has trouble with HIGH SPEED inet and high end encryption. While I wouldn’t sell it on ebay for 500.00, I also wouldn’t recommend any stripped down versions of Linux to a new comer. Suse however I would.