While jezzbb is largely right, there's a program called BrowserChooser that will let you chose which browser is used anytime you click on a link.
Any modern browser will let you save sites as "favorites" or "bookmarks." Most will also import your bookmarks/favorites from other browsers. There are third-party products that will let you synchronize those between several browsers, too.
Firefox, especially with the NoScript and AdBlock extensions installed, is generally much safer than IE. Chrome has gotten to be fairly good, too, and Opera is very reliable. It's a good idea to pick a browser you like for everyday surfing and just use IE for running Windows Update (which requires it).