

I have an X220 with an i5-2520M, I don’t use it for gaming but I have briefly played Half-Life 2 with it and it was comfortably playable.
So I would say mid-2000s titles and before will be fine. It really depends on the age the Thinkpad you want is, and the age of the games you want to play.
I would also recommend openSUSE Tumbleweed. I’m usually a Debian/Debian-based person but I’ve been running Tumbleweed on my desktop for a few years now and it’s been great.
It has a few peculiarities like any distro but it’s been very stable, with few issues even with things like Nvidia drivers. Docs and community seem good too.