i use 'linux mint mate'.. full featured but light enough to run on a system with about 1gig of ram... i have much more than that which makes it even nicer but 2gig is the minimum i recommend if you want to surf the web with a modern browser..https://blog.linuxmint.com/?p=3787
1GB RAM (2GB recommended for a comfortable usage).
15GB of disk space (20GB recommended).
1024×768 resolution (on lower resolutions, press ALT to drag windows with the mouse if they don’t fit in the screen).
it uses so little (i found a p4 w/ 1gig of ram for 10$ at a thrift store that runs it just fine) but is fully featured...
if you are talking about p3 or older athlon machines then you'll need something that uses an older kernel and has been cut down but modern browsers do not run on those cpus... 32bit, 2gigs, and support for sse2, and you'll have a useable machine with linux mint..
'mint xfce' is lighter ui wise but you'll still want at least a gig of ram... 'mint cinnamon' is the heaviest if you like eye candy...