I made some measurements on a nodemcu esp-32s board when I was building my gate monitor. I saw peaks (while wifi tx) of 700mA. This was under worst case conditions of max wifi power and my analogue to digital sensor working.
I reckon if you shot for a 300mA average and had a good sized output filtering capacitor you should be ok.
As for 3.3. vs 5v:
5V will give you an extra layer of protection at the expense of reduced efficiency (may be important in battery powered applications).
Yes, ESP32 requires 3.3 V, well, unless you have a development board with a voltage regulator on it.
About current requirements, the best document about it is its Datasheet
The page 21, 35