Best way to have circuit powered by USB when plugged in and battery when not?
I just asked a similar question here. One answer was what you proposed in your first circuit, but the diodes need to be ideal and the voltages need to be the same. See user 比尔盖子's answer.

The solution I chose was a premade power supply mux from Pololu:

https://www.pololu.com/product/2596

US$5 and does everything I need it to, and can handle different voltages.

EDIT: Also, you will need a buck/boost on the output of circuit to maintain consistent voltage (LiPo won't be 5V exactly so your Vout will jump around without it). I also discovered you need a lot of cap on Vout because the IR droop from the switching will cause circuits to brownout and/or reset.