You've got it a little backwards.
Opera is the one where the free version has ads. Opera is *not* spyware, though. If you choose the text ads, Opera uses the same Google Adsense version that website authors use. So if you currently block Adsense on webpages, you'll block Opera's text ads. And if you don't mind Adsense, Opera's text ads work the same way.
The ads itself is a part of the main toolbar. The toolbar with ad takes up about as much screen space as IE6 with the main buttons showing pictures and text. Except that with Opera you can put things like the status and address bars into the main bar so that one toolbar will be all you need... can't do that with IE!
I'd urge you not to let the ads keep you from downloading Opera and giving it a try. It's small and fast, has great (X)HTML and CSS support, and tons of customizability and features, both in security and regular browsing. They're very quick about security fixes, too.
Mozilla and FireFox are technically different products by the same company.
Mozilla, IIRC, is sort of the "all-in-one" deal. It's past 1.0 at this stage. It's a nice browser... great (X)HTML and CSS support, and a healthy set of features... definitely also blows IE out of the water. I just personally don't use it because I don't find it as customizable or feature-rich as Opera (plus it's a larger download and IMHO a bit clunkier-feeling), but someone who's less of a tweaker would like it.
FireFox is Mozilla's "browser-only" deal. It's smaller and faster than Mozilla and has the same rendering capabilities, but it's also less feature-enabled at the get-go. To add features, you pick and choose and install add-ons called "extensions". It hasn't reached 1.0 yet, but it's a stable and fully-functional browser. (And still worlds better than IE, IMHO.)
Mozilla is also open-source and freeware. So if you see a fix that needs to be made, and you've got some programming abilities, you can roll up your sleeves and concoct something.
I'd really urge you to download Mozilla and Opera and give them a try, Dew. I have to admit I find it kind of strange that someone so concerned about security uses IE as their main browser... it's like walking around with a target painted on your back. And IMHO there's a whole ton of other reasons to switch from IE, too.
Peace & Luv, Liz