2GBps would likely require at a minimum 16-bit transfers using a parallel bus @ 125 MHz, I would probably go to 32-bit just to reduce that clock rate down to 62.5 MHz SDR or stay with 16-bit DDR. It might be better to use a transceiver based solution a single 2.5Gbps SERDES link would suffice. Your budget seems low, as most of the boards Xilinx and Altera have on their website with either high speed parallel interfaces or serial links (transceivers) are price well above that. You'll have a better selection of boards in the 1000 euro range.