Without a doubt google chrome is the best browser. It is the fastest, you can into it with your google account so it syncs your bookmarks and saved passwords across multiple computers, there are tons of awesome free add ons for just about anything you can imagine. Try it out at google.com/chrome
Internet explorer is pretty bad and I don't recommend anyone use it. The main reason is because it is the most used browser as it comes installed with windows so it is also the most targetted browser for viruses and spy/adware.
Aside from chrome I would also recommend firefox, it is very similar to chrome and can do most of the same things but it is a bit slower. A lot of this comes down to personal preference as well.
But in my professional opinion I suggest Chrome.