Attached is a schematic of a board that I designed for the ESP-01.
I adding a diode to the RESET input. The diode discharges the capacitor as the supply voltage decays, so that if power is restored during the decay, the ESP has a better chance of getting Reset.
I also suggest adding bulk capacitance (10uF) in parallel with the 0.1uF at the power supply pins of the ESP8266.
If the ESP8266 will be used without the RxD connection, then a pull-up is a good idea so that this input is not left floating.