I dont think proxies will actually "hide" you on the internet. There really isnt much you can do to do that at all. But the link to that torbrowser thing is probably your best bet, as in the past I have used browsers to surf anonymously however that does not mean it is more secure. It wont prevent you from getting viruses/spyware by any means.
As for someone tracing the computer you are using, if they have the technology to do so that cannot be prevented. Like, if the FBI are trying to find you and you want to use the internet, theres nothing you can do to hide yourself from them