Cost Effective Proximity sensing

ryanmw2002:
I would like to place object 1 on the board. The grid/sensors would then send a message to the arduino that "an object" is on the board.
I would then place object 2, in a different location. The grid/sensor would send a message saying "another object" is on the board.

Ideally i'd like for it to sense if it is object 1 or 2. I know that would be more difficult though. I thought using an RFID reader below the board, then attaching an RFID tag to each object.

I think your best bet for that is a force sensor to weigh the board and the things on the board. If "Thing 1" and "Thing 2" have different weights they could be detected if your weight measurement is accurate enough. I doubt you'll get a lot of accuracy for $20.