Firefox is a good choice as your main browser (One Man's Opinion)
What you should do is uninstall QuickTime from the
Add/Remove Programs.
After doing that, open Firefox, then goto
http://www.free-codecs.com and to the left side, look for and download
QuickTime Alternative.. then install it.
After doing that, open
Firefox, then goto
http://www.apple.com then click on the
QuickTime link. After you get to the page, all QuickTime content on that page should load. That will mean that QuickTime is installed. If it isn't installed, and you get to that page, you will get a message that you don't have QuickTime installed.
If for any reason you go to another site, and it says that you don't have QuickTime installed, just post a link to the video, because I don't have QuickTime either, but I don't get any errors about me not having it when I view videos online, including uTube.
Tip: Just because a site says that you need something doesn't mean that you actually do. I've had messages that told me such, but when I switched browsers I didn't get the messages.
If you don't have this
Firefox add on called
IE Tab... get it. It will allow you to switch from the Firefox engine to the IE engine, eliminating the need to actually open up IE.