Finally, solved garbage symbols in serial monitor by lowering the ESP's baud rate from 115200 to 9600 with the following command:
AT+UART_DEF=9600,8,1,0,0
The root cause of the problem is speed limitations of the SoftwareSerial. On hardware Serial connection, it should work ok with speeds up to 115200.
There is my ESP AT+GMR info:
AT version:1.3.0.0(Jul 14 2016 18:54:01)
SDK version:2.0.0(5a875ba)
v1.0.0.3
Mar 13 2018 09:37:06