How to "implement" an Arduino prototype?
with the breadboard


That phrase right there makes the solution a non-starter. Solderless breadboards are good for prototyping, but are too fragile for use in a final project.

As for whether or not you should use an actual Arduino or reduce the circuit to a minimum, that is between you and your wallet. It is possible to make a basic AVR board (including MCU) for under $6 in parts, but the time investment is not entirely trivial.