I would either go with either firefox or opera ( IE has a lot of down falls with regards to spyware / bugs ) that can easily re direct your page to dodgy sites.
Look at www.hijackthis.de and also search for a tutorial on hijackthis just as one example.
Firefox and opera are -
1 - faster browsers because they give you the browser with out all the add ons that microsoft think you need but dont really and you can download and install your own add on bits from there websites.
2. Are a more secure because they are updating them a lot more and are less likely for things like above to be installed without the users consent.
With regards to comparing opera and firefox - best to try them both out for yourself and see what you think as everyones personal opinions will differ. Hence personal preference, I could say firefox and the next poster could say opera.
Most web site designers ( if they are good ) will ensure that there website is compatable between browsers regardless.
Most users use IE because they are not computer literate and because IE comes as standard and so they just go along with it, that or they are using a work computer or laptop and IE is more inbuilt with the windows operating system and so easier to control with regards to restrictions ( although saying that firefox has got an admin template )
Not sure how well it works though.