If you're interested in optimizing, the Dohm classic "sound machine" isn't very expensive (maybe 2x what a decent fan costs), is portable/packable, has tunable sound, but is fundamentally just a fan that doesn't move air around your room.

It's different for different people. The air purifier method suggested works for me, but any fan is better than no fan.

You can buy an air purifier, like IKEA FÖRNUFTIG.

Air purifier white noise is the best. I don't know what it is about it.

It's cause the noise is filtered

Agreed (provided it is a sufficiently large air purifier like Austin Air's Healthmate).