ESP8266 Wifi issues with Serial monitor? Exception 0?

Pretty much, but one of the things you can find out is what type of flash is on the board. Simply read whatever is written on the flash-chip (that is the 8-pin IC) and google that.
I don't have the same esp-core installed as you so i don't have the same options in your menu, most of the options will be fine in their default setting.

Just to make sure that you don't have anything connected to the units GPIO 0, 1 & 2, which should not be pulled "LOW' at boot, but i think the issue is elsewhere.