For browsing the internet you could look into using Tor. It's not something you should take lightly, as you shouldn't take sending anything through a proxy lightly unless you own the proxy and can therefore control it. There are risks of people discovering you through sub-conscience patterns and leaked data that you didn't secure. For example, in some countries if you go to facebook you are risking your freedom and your life, so if you were one of these people I would tell you that it's probably not worth it. On the other hand, if you just want to check out a website while keeping some privacy, then you should check it out, read what you can, know that it's possible someone is listening in (as they could on any line you don't control), but likely different people than had you not used Tor.
As far as security, you can browse the internet using a linux LiveCD, then you are sure you're not picking anything up, as the operating system is booted off the cd where a website/virus presumably can't save anything.
Torrents are a bit of a different beast, in that the most common answers are to get a seedbox or a VPN if you don't want your ISP listening in. Either are probably fine, mostly comes down to preference.