Good questions here:
First, the best way to reach the broadest number of participants is to select all of the technologies (click once, java webstart, activex, mozilla plugin) and let the launch page try to determine which will most likely work.
Second, there is no need to push participants to use IE or Firefox - they are both equally functional. If you were targeting a specific set of computers and knew what was pre-installed on them, you might be able to optimize for one browser or the other, but if you are targeting PCs in the wild, neither has a clear advantage. Note that the Safari and Google browsers work as well, although there are a few minor bumps in these cases.
Third, on a majority of computers, Inquisit can be installed and run by normal users without administrative privileges on their computer. The only exceptions are computers that 1) don't have Firefox 3 or later AND don't have java 1.5 AND don't have the .NET Framework 2.0 or later. Only if all three conditions are met (which is increasingly rare) will users have to be an Admin on the machine.
Finally, if participant can't get the study to launch, point them to the links at the bottom of the page under "Having trouble starting?" These will allow them to try a different download method if the first didn't work for some reason.
Hope this helps,
P.S. Fifth, Inquisit does not currently run on the Mac. I am madly coding away to get things working on the Mac, but it's a ways off yet.