great first project
Actually you may need to throttle back your expectations. This kind of device is not like a USB camera - if you want a USB camera, I’d suggest you buy a purpose built one and keep your Gadgeteer kit for other projects. If you just want to do this to prove you can, then that’s fine, lets keep talking.
I’d break this down into a few different tasks. And the LAST thing to think about is what connection you’re going to use.
The first thing you need to think about is how are you going to view the captured image - ask yourself questions like do you have an application that saves it to disk and you manually open it, or do you expect it to be displayed in a browser? Really you need to explain what the use-case is because that helps set the direction for all the possible options. And in your question you talk about speed - what is that important ?
The answer to your question is likely to be Ethernet, but that doesn’t mean anything until we really understand your use case. There are many reasons that you would choose any or all of those module options, but it totally depends on what you need.