I have 4 browsers installed on my computer; IE, Firefox, Google Chrome and Safari.
I would recommend Firefox and Safari, I use both them regularly.
Firefox is a very good browser, I didn't have any problems with it at all, and it has a lot of useful add-ons.
Safari is very easy to get used to, and runs just as Firefox, really good.
Google Chrome is also a nice browser, but I don't use it much because I don't really like the looks and I have to refresh some site before I can see them..
Just try some browsers, and then keep the one(s) that you like the most.