This answer is based on the OP's question. mainly taking into account
but what I'm theorizing it that this could actually be a product that
could be sold on shelves.
Well this is how i would do it - if i were forced to use and Arduino instead of an Arm based chip.
If you are going to host a webserver on the chip, then you need to write some admin code for it too.
By default you would have the actual device you are building HOST peer-to-peer WIFI connection over an unsecured network. So you can use any laptop and connect to to it.. Viola- You are in the system without any LCD on the Webserver that you designed.
In the admin panel of the webserver you would have a script/page that scans the netowork for aviable network points, lets you choose one, enter the key and click save/connect.
Your disconnected form the peer-to-peer wifi connection and your arduino connects to your wifi and aqcquires a new IP via DHCP. You then have the device configured.
Since a comment says that ad-hoc might cause wifi scanning issues jsut prooved the arudino is not a great way to use wifi with. You would need your computer to scan the WIFI- then pipeline it to the arduino with the correct settings- entered manually- reset and then
Keep in account there needs to be a reset button on the arduino to reset back to peer-to-peer mode incase you change your network or your router dies and you get a new one.
Using Arduino i assume you will have an WIFI shield, and a WEBSERVER Shield driven somehow to ineterconnect all this mess into something useful?
Problem with Arduino is that it is really bad at handling anything more than drawing some nice shapes on a small LCD screen.
If it was me- I would find a chip based on the ARM that uses the same C code that Arduino does but has got 32mhz/64mhz or 100mhz - which makes working with WIFI allot faster , and especially using lighttpd+php5 on a tinyLinux(as light as 2megabytes with pre compiled drivers into kernel) on it will be greatly improved and save you years of rewriting device specific codes and networking protocols.
You can then interface with the WIFI network faster than the 115kilobaud that serial will allow you on the Arduino.
Those chips do not cost much more than an Arduino and there are tons of code snippets available.
Another option would be to use a BlueTooth module that will connect with PushButton Authentication and write some software for your Android/iPhone or Server on your Netbook that connects via SPP (Serial Port) - You can get Bluetooth Modules that have upo to 20 Metre range with a bigger antenna and boosted signal. That would be more feasable way to control an Arduino without having any front end (webserver) at all!
When you come to realise that you want to realise this to the market and find that using a LCD screen and all the necessary things that go with it-- increase your cost "just to connet to wifi" - thats when you wills start asking your self- how to get rid of all the un necessary bits and bobs.
Dont reinvent the wheel. The Arduino is too weak to be released for anything more than a wireless temperature monitor on 433mhz..