To clarify and expand on Andrew's answer:
Manage content through
amazon.com/myk where you can view items and organize into collections.
read.amazon.com to read material from a browser.
Or, use the
kindle app on phone or tablet to both manage and read content.
It's not quite, but almost, a 1:1 relationship between an e-ink kindle device and the cloud. Most everything will be synced and available both. Changing or re-organizing on either will sync to the other.
You don't need to buy a Kindle e-ink device, or Kindle tablet. You might want to, at some point. This is DRM lock-in analogous to iTunes et. al. so that once you pick your poison it's just easier to stay in that walled garden.
(For what it's worth, take a look at e-ink readers-- very interesting.)
You can delete material from a device and leave it on the cloud reader. Or, delete from both device and cloud.
Some material, here and there, won't show on your e-ink device because it's not compatible. Not an issue for this Kindle user, and a very minor "gotcha".