don't know a board but can tell a bot about the protocols
I2C supports multiple devices, so choosing I2C will not "harm". Drawback is that it is relative slow.
SPI is much faster, but you can only connect one device (every extra device needs an extra chip select)
If you have SPI free for your project that might be preferred.
How about a promini?
I also offer a '328P & '1284P board with extra power & gnd connections, but no voltage regulator if you have a 5V supply. http://www.crossroadsfencing.com/BobuinoRev17
OP needs 12-bit ADCs, which rules out the AVRs, provided you need actual 12-bit ADC, ie, oversampling per Atmel App note AVR121 http://www.atmel.com/images/doc8003.pdf is not sufficient.
My suggestion would be to either buy another Teensy, or (if it isn't too big) try the Maple Mini. It got great support, and cost less than 4$. The board got 34 IO pins and 9 12-bit analog inputs. It also got 3 serial ports, 2 i2c busses, and 2 SPI busses.
and it's REALLY fast compared to an Arduino UNO