ESP8266 gives junk over serial
I have tried one of the ESP8266 boards, I cannot say for sure if its exactly the same as yours, but it looks similar. This is what I found:

The initial boot up text is sent out at about 76900 baud. I had to get a scope and measure it at 13us per bit.

After the initial boot up text the board changes to 115200 baud, and I could then send commands to it. Initially I had some problems using PuTTY, I couldn't get PuTTY to send the correct end of line sequence of CR, LF. Using the Ctrl keys I could send A T ctrl-M ctrl-J and get back a response of "OK". Since then I have used Hercules, partly because in addition to the terminal emulator it also has TCP Clients and servers which make it easy to try out the ESP8266.