WanderingPlotor said: Does it work to purchase backwards compatible games on the web-based Xbox store, and then download to 360, or does it have to be on the One (and newer) consoles itself?
You can buy where you want. The purchase is saved in your account. You are accessing the same store. No matter if you are using a windows app, a web browser, a phone app or one of the may xbox one / series consoles.