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?
Given what is available in assembled form, using a complete commercial product per project would make most sense except where you are building in substantial volume.
I am using Arduino Nano 3s from China which cost me $US3 each in quantities of 10 with free postage (takes 2 to 3 weeks to arrive here at the bottom of the world) and I see that the same people are now charging $2.85 each in 10's. There are numerous suppliers of similar products and I am only mentioning these as I have had good results from them and the quality is acceptable.
You would probably have trouble buying just the parts for the cost of a $3 assembled working Nano and you'd need to cost your time at $0/hour. Building your own for the experience, or if you are using many and you want a cut down subset and really must get the price well under $3 MAY make sense.
The same people also sell an Arduino Pro mini for $US1.85 in 10s free postage (ie $18.50 for TEN). You need to use a plug in USB module to program these via USB. I bought some of these as well - also good, but the convenience of the always available USB makes the Nano preferable (to me).
Note: USB cables cost extra !!! :-)
Some people have expressed reservations about buying Asian source Arduinos and suggest people should support either US fronted companies or the Arduino's originators.
I appreciate the merit of supporting the people who have put the effort into the system, but the system is very very consciously open source in all respects - and in fact code samples that come with the IDE are expressly Public Domain. (Documentation is CC by SA ...). If open source is to be truly meaningful it needs to be able to survive being truly so. Unlike many other products where Asian copies may have suspect IP legacies, the Arduino products are wholly legitimate (as far as I know).
I have not pored over them in detail (yet) but I note that the 5V voltage regulator on the Chinese ones is an LM1117 (LDO LM317-like) as opposed to the original LM2940. The USB bridge ICs are, as is well known, not "genuine" FTDI parts but Asian semi-equivalents which, with their own drivers, work well enough in this context.
You can certainly buy low cost rubbish versions from Asian sources, and part of the open source tradeoff is deciding where you do and don't get value for money overall.