Using an Ethernet is good and universal way to send data to PC, however it would require more than just hardware and low level software. The easiest way using FPGA would probably be by implementing NIOS II soft core processor and software TCP/IP stack (also some kind of real time OS would be needed together with the TCP/IP stack). I think Altera provides such an example as a template design using uC-OS for DE0-Nano SOC. You should have in mind that uC-OS with it's TCP/IP module has relatively expensive licenses.
You can also check some kind of additional controller between the board and the PC which has already developed drivers. For example FTDI's chips like FT2232H (
http://www.ftdichip.com/). Particularly this one provides USB to MPSSE interface with ready to use drivers for the PC. They say it can achieve up to 30Mbsp. However here you would need to make additional hardware.
Victor