Webcam + LED microcontroller
So the webcam image is processed by a computer, which then tells the microcontroller what to do with the LEDs?

It seems like there are two completely separate parts to this project - a webcam and a microcontroller controlled LED display.

For the webcam: buy one that you like. We're not going to do your shopping for you. It has absolutely no bearing on the microcontroller, it's a webcam plugged in to your PC.

For the microcontroller - you have two broad choices - one with USB built in, and implement a USB stack in the MCU, or one with UART and use a USB to UART bridge, like an FT232 chip.

Which one to choose?  Your guess is as good as mine.  Pretty much any of them can interface to the computer either through USB or a USB to UART bridge.  Any of them can drive LEDs.  The task is a very simple one, so you don't need lots of memory or flash, so nothing fancy is needed.

And yes, a USB hub will connect both the webcam and the microcontroller to your computer.