Arduino + WiFi ESP8266

Can anyone help me with communication between Arduino Uno and ESP8266-05?

I've this simple code only for testing response:

#include <SoftwareSerial.h>

SoftwareSerial esp8266(12, 13);

void setup () {
    esp8266.begin(19200);
    Serial.begin(115200);
}

void loop () {
    char buffer[50];
    esp8266.write("AT\r\n");
    esp8266.readBytes(buffer, sizeof(buffer));
    Serial.println(buffer);
    delay(1000);
}

But the response is some junk (in Serial monitor on my PC):

1_Q¨ (X1JXþUÉÁEóAñ¡5%¥4¡1!!1%%¡5%¡4¡1¡!!G-]5

This behaviour is the same if I'm using a simple resistor voltage divider or level shifter (http://www.banggood.com/5-Pcs-3_3V-5V-TTL-Bi-directional-Logic-Level-Converter-For-Arduino-p-951182.html).

Connection:
Arduino - esp
pin 12 - pin Tx
pin 13 - resistor divider 10k/20k - pin Rx

OR
Arduino - (HV) level shifter (LV) - esp
pin 12 - TxO - TxI - pin Tx
pin 13 - RxI - RxO - pin Rx

ESP reset pin - not connected

I don't know what's wrong, because when I turn on the Arduino and ESP module, I see on my notebook a new wifi network called AI-THINKER_012568 and I can connect to this network.

I supposed, when I turn on the ESP module, I should get a 'ready' response, but I get only some junk data. So, for the 'AT' command, I should get an 'OK' response...

I searched a lot for troubles with character set (ASCII vs UTF), but without any results.

I've tried a lot of combinations with reading (read()) and writing (write(), print(), println()) data from one serial port to another, but only with some junk response or without any response... I've tried various baud rates too.

Bonus question: when I searched for some manuals, I've only found manuals with ESP8266-01, so, is ESP8266-05 worse than the first version or is there something wrong?

Edit:

When I've simple code for arduino, which only sends data from one serial port to the second port:

#include <SoftwareSerial.h>

SoftwareSerial mySerial(12, 13); // RX, TX

void setup () {
    Serial.begin(9600);
    while (!Serial) {}
    Serial.println("€");

    mySerial.begin(9600);
}

void loop () {
    mySerial.listen();
    int i = 0;
    while (mySerial.available()) {
        char c = mySerial.read();
        Serial.write(c);
        i++;
    }
    if (i > 0) {
        Serial.println();
    }        


    int j = 0;
    while (Serial.available()) {
        char c = Serial.read();
        mySerial.write(c);
        Serial.print(c);
        j++;
    }
    if (j > 0) {
        Serial.println();
        mySerial.println();
    }
}

And when I upload code and turn on ESP microchip, I got something like this:

â-¬

ÿ
q·$aã
Å% ð´
D9$kvKþµ¿`ÈÛ¯h:¤ó[Y \B¡H$èðÍÝ׸Jø
å
ü+¡
ð

First line is for '€' character, only for test. Next lines are initial response from ESP microchip. As I read in ESP documentation, when ESP microchip starts, I should got some data about version and ready word. Means these lines, that ESP microchip is death or only there is something wrong with reading this response?

Then when I sent 'AT' command, I got no response :(