/diy/ - Do It Yourself

Very basic question here:
I have 16V (or so) AC and need around 3.3V DC. I thought about using a diode bridge to turn AC into DC, like pic related and then a Resistor to drop it to 3.3V.
Three questions:

1. What DC voltage will I have after the diodes? Wasn't there something like a factor of √(2) or something like that?

2. Would some generic 1N4148 diodes work?

3. What resistance would I need to get 3.3V? I thought about using kirchhoffs voltage law, so I would know the voltage that the resistor is supposed to drop is X-3.3V where X is the supply voltage. I can't solve U=RI though because I don't know the current needed. I don't know the current drawn/ the resistance of the ESP8266 I want to power either so I can't calculate it. Any thoughts? Thanks.