For any real suggestions, we need more information.
You say that you have most aspects figured out. Is your bot going to be moving around, or just hitting a ball that comes straight to it?
Neither an MCU or arduino(it's MCU based) will be able to do that kind of vision processing. I'm looking into the capabilities of the Raspberry Pi, a small $35USD Linux computer, for vision processing. You might want to check it out.
Why is sending the video to a laptop out of the question?
This is a huge project, even for an experienced roboticist. If you're serious about completing it within a year, I'd suggest making it a team project, and preparing to spend a LOT of money trying and failing before you get it right. Come up with 10 (or more) ideas, build them all, leave behind what doesn't work, and splice what does.
Good luck, and don't forget to keep us posted.