If you want to run a modern current linux distro on a laptop with only 2gb of ram and 500gb then your options are very limited, but it is possible.

For example. Void Linux with Enlightenment will work. A browser will work ok for basic websites but heavy apps like Gmail will be unusably slow.

If you have no option to upgrade, you can still use a machine with those specs to run linux apps like Abiword, Gnumeric, GIMP, etc very well.

Also, putting in any SSD drive to replace the spinning one is the single best upgrade you can make in terms of performance and longevity on an old laptop.