Unless you got that model number wrong, the T420 is not an old machine, only just over a decade of age. Any Linux will do as long as you aren't running GNOME with it.
Yeah I had a T510 before I gave it away and honestly save for the slow hard drive it was a competent little machine for web browsing and such, and it still is, if you upgraded the RAM slightly and ditched Windows. It doesn't get bad until you go into the Core 2 Duo or weaker circa 2005~.
Just don't expect to be playing games on it though if your OEM didn't give you a discrete video card. Intel HD Graphics from this time period were terrible. Some of these ThinkPad models came with GeForce cards but then sometimes you got a bad one from some office and at that point you've got a homework machine.