Random characters transmitted from ESP8266 to Arduino
The baud rates, voltages, and timing all have to match up for serial communication to work right.

So, set both of your devices to the same baudrate (you specify the number in Serial.begin()), and ensure they're connected properly. (voltages match, TX to RX, and ground is connected)

You can just read/print the serial input to the arduino with something like Serial.print(softSerial.read()) in your code if you think you don't have serial wired up right.

Also in an unrelated issue; the esp32 spits out data on its main serial line at 115200 when it boots up which you can not disable. you can use the serial port afterwards though.

Here's a copy of what gets printed out on one of mine;

rst:0x1 (POWERON_RESET),boot:0x13 (SPI_FAST_FLASH_BOOT)
configsip: 0, SPIWP:0xee
clk_drv:0x00,q_drv:0x00,d_drv:0x00,cs0_drv:0x00,hd_drv:0x00,wp_drv:0x00
mode:DIO, clock div:1
load:0x3fff0018,len:4
load:0x3fff001c,len:1044
load:0x40078000,len:8896
load:0x40080400,len:5816
entry 0x400806ac