What to do after prototyping?
Yes, your thinking is pretty much correct.

You can place an ATMega32U4 chip and the associated required circuitry within your own circuit design. The required circuitry is actually quite simple - a crystal for the CPU clock, a few capacitors (load capacitors for the crystal, and decoupling), two 22Ω termination resistors for the USB bus, and a 10KΩ pullup on the reset pin. That's about it (besides power of course).

As far as programming goes, you can either install a bootloader (butterfly - like the Leonardo etc) that works through the USB, or you can directly program the chip using ICSP. It's best to provide an ICSP header anyway (it's the SPI pins plus RESET basically), and if you have done that (which you'd need really to be able to get a bootloader on there) then you may as will skip the bootloader entirely and just program direct through the ICSP header. Of course, you'll need some kind of programmer (an Arduino can do the job at a pinch, but it's worth spending the $10 to get a cheap AVR programmer from eBay).