How to "implement" an Arduino prototype? I am starting with Arduinos, coming from the world of Linux (with the RPi as a bridge) and after having tested some setups I now wonder where to go next in implementation.

What I am trying to understand is whether it is recommended (time and cost-wise) 


to create a standalone, circuit-board based version of whatever I prototyped on the breadboard, with a micro-controller with connections trimmed down to what is needed for that specific setup?
or rather just look at neatly packaging the Arduiono with the breadboard and wires in a case?


I expect to build 5 or 6 of the same simple setups (to put in various places in my house).

Note: there is a similar question (with almost the same title) but it deals with the legal aspects of commercializing a setup.
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.