It depends. IE6 tends to start up faster than Firefox (on first launch) because it shares quite a bit of code with explorer.exe, the shell of the OS. As far as page loading times go, I personally haven't noticed a significant difference (Fx might be a wee bit faster), probably because I'm usually on a good broadband connection - most pages tend to load up almost instantly on either browser anyway. You might notice a difference on lower bandwidth connections.
The Firefox installer is a pretty small download, and once installed, it won't interfere with your IE6 installation in any way. I encourage you to try it out and decide for yourself.
All the browsers available on windows are pretty much as secure as each other.
Opera and IE are your best bets. Mozilla has a sort of "holier-than-thou" attitude at the moment. Either you do things their way or not at all. They also like claiming credit for things that MS and Opera developed a while back