I posses an extensive knowledge on computer vision, pattern recognition, matching and tracking. I am also an enthusiast of all of this concepts and find great joy in finding solution that are both, practical and elegant.
I have a clear implementation plan for this proof of concept, with algorithms I have tried and know to work with.
I am also based in Europe, this will make communication easier.
Now to your questions:
1) The absolut easiest card design would be a QR code or barcode*, BUT that is also extremely boring and unaesthetic**. My approach would be to code the 10 bit of information (1024=2^10) information in a colorful circle (design consisting of 3 colors+ black or white) which could in turn be printed in a business card or carried as a tag.
2) For this proof of concept I would be using Matlab because of it's speed for developing this kind of prototypes. I can too use another language of your choice (C++,Java, or Python), but this would cost me more time and I would change the price of the bid to something around 600£. A library like OpenCV is indispensable for such an algorithm, not using that would skyrocket the price and time of work.
Hope to hear from you soon.
*Using diverse software libraries available on the internet, the implementation of such an algorithm shouldn't take longer than an hour or two, and require amateur level of programming.
**As an employee or user I would feel horribly objectified with a bar code for identification