Chrome is the browser that was developed by Google.
I don't care for it myself, but some people like it. If you want to try it, you can get it here --> https://www.google.com/intl/en/chrome/browser/
If you don't like IE and Firefox, I'd recommend trying the Opera browser, which you can download from here --> http://www.opera.com/
All browsers will have security updates, but hopefully Opera won't bother you as frequently as Firefox.
You could also try Seamonkey, which is similar to Firefox but seems to have fewer updates (in my experience anyway).
You can get Seamonkey here --> http://www.seamonkey-project.org/
Both Firefox and Seamonkey can use Adblock Plus, which might help if you're being bombarded with ads.***Adblock Plus for Firefox******Adblock Plus for Seamonkey***
Bing and Yahoo are not browsers. They are for doing web searches. It sounds like whatever browser you're using may be asking you which one you want to use for a search engine, and since you're not choosing any of them, you're being asked every time you start the web browser. It's also possible they're asking to install a toolbar or "Active desktop type thing." If that's the case, ad-blocking software would help.
If you can't tell what web browser you're using now, your computer may have come with some extra software that's sitting between you and Internet Explorer. A screenshot of what you see when you try to get to the Internet would help.