Flash hasn't been an issue for quite some releases in Ubuntu.
Your personal experience doesn't make it true for everyone.
The official flash release has to be run through nspluginwrapper on 64-bit systems, which can be a pain when it doesn't work. Suggesting that the average user stick with the 32-bit release removes any support issues related to 32 vs 64-bit plugins (java included too) and nspluginwrapper, with no noticeable drawback for most users.
I would know, because I've never installed Flash manually on this system.
What I'm saying, is that flash, java (plugin), and nspluginwrapper can be broken. It happens; and when it happens, it's not obvious what went wrong or how to fix it. Going 32-bit simply removes this support issue altogether.
If you want to address > 4GB of RAM on 32bit, install the PAE kernel. I think the meta package is called linux-generic-pae.
Use 64bit if you want to run applications that will benefit from it.
EDIT: If in doubt, use the 32 bit one as it will give you less friction for general purpose desktop use.
http://journal.dedasys.com/2008/11/24/slicehost-vs-linode
At least for some things, in my experience.