WW,
Did you ever get Links 2001 running with the 1.22 patch? It makes absolutely no difference where you save the files when you download them. It only matter where they "point" when you run the patch. Typically, the patch will look into your registry to determine where the game is installed and the patch will attempt to overwrite (i.e., patch) the files in that directory. However, Vista (and Win7) have added security that didn't normally exist in WinXP. That additional security prevents users from changing files in the "\Program Files" directory. Instead of writing the files into "\Program Files", they write the files into the "\Virtual Store" directory, which is tucked away in an inconspicuous location.
You can "bypass" this additional security by running (trusted) EXE files with "Elevated Administrative Privileges". While it sounds a bit ominous, it's really not. All you need to do, is right-click on the EXE file for the patch, select "Properties", switch to the "Compatibility" tab and then check the box that says "Run as Administrator". Then, when you double-click on the patch EXE, it should start and write the files to the correct directory (usually C:\Program Files\Microsoft Links\Links 2001\, or whatever directory you installed the game in). Make sure when you run the patch, that it points to the same directory where the game is installed.
As to which version you require, it may depend on the version of the game you have installed. CE is the "Championship Edition" of Links 2001 and, to be honest, I don't know how/if that is different from the regular version. As per the instructions on
http://www.linkscountryclub.com/links-2001-updates, you will need to be running v1.21 before installing v1.22 as well. So, first download and install the 1.21 patch (from the bottom of the page) and then install the 1.22 version. Use the method described above to install both patches (in order) with elevated administrative privileges. I usually start the game after each patch and check to ensure that the patch was properly installed by checking "About" in the menus within the game.
Let us know if this has helped and if you've been able to get the game installed and running.
Armand