I want to use a MCU, not Arduino, to receive some data and send through ESP8266 via WIFI to another ESP8266 via WIFI.
Both boards will have a MCU and an ESP8266.
My question is, how do I do this without having to program a custom firmware to ESP8266? I want to use it as it comes.
What's the peripheral(I2C, UART, SPI) that I may use for it?
Your questions seem a bit unclear to me.
NodeMCU is firmware that runs on ESP8266, and is programable in Lua.
You will not have to design your own firmware, of course, but flashing a ready-built custom firmware onto an ESP8266 is a trivial task and you have to do it, since most of the firmware available on the market chips is pretty ancient.
Once you have that set up, the you can program the chip with IIC, SPI, UART, wifi or whatever, these are NodeMCU libraries, NOT peripherals, and they are built in to the chip via the firmware.
All you have to do is use basic Lua to hook up the protocols you want to use (that's up to you), You'd probably end up using wifi and http or tcp.
Do some more reading up to get an idea, the scope of use is pretty huge, and that's without even going to the Arduino/C route suggested by the poster above me.