The AMD64 processors are designed to be backwards compatible and the x86_64 architecture is considered a multilib architecture. AMD64 processors are capable of using 32- or 64-bit code. If you use a standards compliant OS, then it will also support 32- and 64-bit ABIs. Everything will happily co-exist and you simply need to double-click the icon for the 32-bit application or the 64-bit application. I do not know whether Ubuntu is standards compliant.
Off the top of my head, I can't think of any browser plugins that are available as 64-bit libraries. You can use the 32-bit plugins with a 64-bit browser by using a wrapper. It's probably easier to simply use a 32-bit browser instead. You won't notice the internet moving any faster using a 64-bit browser anyway.
You, as a human being, will not notice the differences between 32- and 64-bit unless you are doing something that requires millions or billions of calculations. Video editing, large engineering, scientific, and mathematical simulations will provide noticable improvements; you will see tasks that took 15-minutes using a 32-bit application take 10-minutes with the 64-bit version or a simulation that took 40-hours to run on a 32-bit machine run in 33-hours on a 64-bit machine. You won't notice the three nanoseconds you save loading a webpage or opening an OpenOffice document.
There are very few 64-bit Windows applications and I suspect you will be using 32-bit Windows software anyway. From what I have read, it's not worth the trouble using the 64-bit Wine given the few 64-bit Windows apps. Use the 32-bit Wine for your 32-bit Windows applications.
I would find a standards compliant distro and install 32-bit Wine, 32-bit Firefox, 32-bit mplayer (multimedia codecs is another area lacking in 64-bit support, but that is improving), and 64-bit everything else. I recommend that because that's what I do, but why limit the capabilities of your hardware by using a 32-bit OS? The hardware is designed to allow you to use both ABIs side-by-side. If you want to limit the capabilities of your hardware, use Windows instead.