As for firmware, my ESP has only 4Mbit (512K), and I found a web page that says 1.5.0 is the last version that will run on a 4Mbit board. I just searched around again, and found that https://syonyk.blogspot.ca/2016/11/installing-latest-at-firmware-on-4mbit.html documents putting v2.0.0 on a 4Mbit (512K) module. But when I check the Readme for v2.0.0, it says "Please be noted that with the release of NONOS SDK Version 1.5.0 (ESP8266_NONOS_SDK_V1.5.0), the space that AT commands occupies has increased to more than 4Mbit. Therefore, flash with 4Mbit capacity is no longer supported. Please choose flash with at least 8Mbit capacity. ", so I'm really not sure how this worked.
QuickFix wrote:What atexit8 says: the ESP is very picky about power.
Make sure it's a stable 3.3V and can provide enough current (>500mA, but preferably 1A to be on the safe side).
Do not trust your USB -> RS232 TTL board is adequate, since it most of the time isn't.
Also: some bugs are resolved since version 1.5, you might want to try the latest firmware version (v.2.1.0 at the moment).