simultaneous processing of 4 IF signals
But I am not able to decide on which microcontroller will be best for simultaneous data acquisition from 4 channels of ADC using SPI.


Read and understand the datasheet of your ADC. You will use SPI to configure and control this ADC, but data is delivered on dedicated outputs that can also operate from an external clock (slave mode). For the control part, a low end microprocessor is appropriate. Storing and/or transferring data to a host is stream processing, a uC adds no benefit, an FPGA would be better.


  Apart from acquisition I have to run a separate process to transfer the data to PC via RS232 or LAN. 


RS232 will be too slow, Ethernet and USB are common for this purpose. Sending data in Ethernet-frames to a configurable MAC without any protocol is a high-speed solution with very little overhead (but does not allow for a routed connection). USB may need more effort, I suggest looking at Cypress EZ-USB products if you want to go that way.

On FPGAs, IP for DRAM-controllers and Ethernet is available for free. Free NAND- and NOR-flash controllers might be harder to find. A FPGA can also host a simple uC, either as hard-IP or as soft-CPU. 


  Please suggest ...


I suggest a DE0-nano SoC for development (cheap). It has GPIOs on pin headers (HSMC connectors are more expensive and do not add value at your data rate). Put your ADCs on a daughterboard. Use the dual core ARM Cortex A9 hard-IP for control. Implement data streaming to DRAM and Ethernet in the FPGA-fabric.