It's a bit confusing to be honest...
... later when the application is ready I expect to install it in 64
bit or in 32 bit machines.
All 32-bit applications also work on 64-bit, because Intel/AMD made their AMD64 implementation backward compatible. In other words: regardless if you're using unmanaged or managed code, you can always run it on a 64-bit platform.
The other way around that's not the case, so:
if I design the application under 64 bit I think it will not work
under 32 bit, right?
Yes, correct.
Personally I don't bother anymore with x86 because everyone nowadays has a 64-bit capable processor.
It's usually best to compile to 'Any CPU'. The 'x86' and 'x64' targets are only there to enforce a certain platform. In practice everything is always compiler to .NET IL - which is JIT compiled by the runtime to native assembler.
The JIT uses the 'target flag' or the 'prefer 32-bit' (csproj properties) hint to determine which runtime should run the code. If
- you have the 'x86' target or
- 'prefer 32-bit' (default) or
- if you don't have a 64-bit system and don't have the 'prefer 32-bit' checked
it will use the x86 JIT compiler (and runtime). Otherwise it will use the x64 JIT compiler (and runtime).
There are some differences and subtleties that you change when you do this (that all have to do with native interop), but when you stick to normal C# code you shouldn't notice them.
Summary: Personally I seem to make it a habit of not being able to fit my application in 2 GB of RAM (I work what they now call 'big data'), so in those cases the best practice is to use the 'Any CPU' target and uncheck the 'prefer 32-bit'. That said, if you don't need the memory, it's probably better to leave it on as a safeguard.
my question is: if I design it and then create
setup file under 64 bit computer, what should I do later in order for
my application to work under 32 bit windows machines?
You might be surprised, but that's actually a totally different question. Setup systems (e.g. MSI) are highly dependent on the operating system. Most MSI's therefore use hacks to make it work on both platforms. Wix has some quite good documentation about this.