Determining the features of the DSP I need to sample a signal of 40MHz with a sampling frequency of 120MHz at least with a 8/12 bits ADC and send them through the USB serial port of a PC. That means the serial communication bandwith should be at least 960/1440 megabits per second. 

What kind of DSP should I use to satisfy this bit-rate, and what signal-processing-methods should I learn to optimize this bit-stream to use the same data simultaneously with a mainstream PC. (The bitrate seemed a bit huge for me.)

I have no experience with DSPs before. I was seeking for answers for a while but not even my teachers, or their assistants could help me for a little long period of time. 

I just need a beacon to find the answers of the questions, thanks in advance.

Edit: I wrote 40Hz instead 40MHz, I am really sorry.
This doesn't sound like you need a DSP at all.

You'll need something that does USB3 towards your computer. Typical solution to that is the fx3 chip from cypress. I'm not aware of DSPs that integrate a USB 3 phy or even just the logic to speak to one - not a typical interconnect in their world.

Then you need something that orchestrates the ADC, keeps timing correct, and hands over the data to the usb3 chip, but doesn't do much of actual signal processing.

The whole "glueing one high speed digital thing to another" aspect screams for an FPGA. So, what I'd recommend: pick an FX3 development board and design an FPGA/ADC add-on board to that.

May I also interest you in other interconnects? Maybe gigabit Ethernet is sufficient for your use case; in that case, you could basically use the Ettus N200 as reference design (schematics are public). Or buy one - it comes with a dual-100MS/s ADC, and with the BasicRX daughterboard, you can directly interface with that ADC in baseband. 

Full disclosure: I'm affiliated with Ettus, but to be honest, I'd like to see you succeed in building your DAQ device :)