The original request was specifically for white button-downs, and all the brands featured here make great ones. But I am not a skilled enough writer to come up with varied and creative descriptions of a bunch of items as essentially identical as classic white button-downs. So I broadened my search to include all button-downs, and a good place to start is Frank & Eileen, specifically with the Joedy shirt, a roomy boyfriend-cut number that comes in a number of good colors and weights.
Nili Lotan makes divine (and, I know, stupidly pricey) button-downs, and I mostly buy them on resale sites. But very occasionally I’ll splurge on one, usually because it has something cool or interesting going on. Like this this perfectly slouchy tuxedo top. (Here’s simething similar and much, much cheaper).
J Crew offers a whole ton of decent button-downs, most of which go for a little under or over $100. I like this white one for times when I want my shirt to be roomy but not too roomy.