App for collecting (and categorizing) stuff from the web

I've looked high and low and I'm surprised I haven't found exactly what I'm looking for; it seems like such a common task.

I just want an iPhone app to rapidly clip stuff from web pages. My first priority is just to clip images (with source url and/or caption). But being able to do the same with bits of text, links, videos, etc would be nice.

The way I imagine it working is: I navigate on the web. I hold down an image or selection. Some "drop points" appear on the side for me to drag and drop it into. I can have as many drop points as I want and they can have names.

More abstractly: I just want a very gestural/natural way (i.e. doesn't require thinking or tapping) to grab stuff from web pages and put them into folders.