Firstly depending on your local laws you'll want to encrypt your hard drive using something like truecrypt etc. United states law I think pretty much doesnt make you give up your passwords for it (unlike the UK) . But even if some states do or whatever, TrueCrypt has a decoy function that makes it impossible for feds etc to prove that youre lying about the existence of another crypted disk (makes more sense if you have it)
There are other less drastic options, like you can download a portable browser and put that into its own crypted volume (So basically it just shows up as a random file with your choice of name and extension .jpg, .exe etc. only you know what it really is and only you can get in with a password.) but although that works well against the average joe, browsers have a habit of leaving traces of just about anything in separate places all over on your computer, and going around and manually erasing them isnt practical or effective, even with software designed to securely remove.
As for internet, proxys are good on paper, but most proxy companys will easily fold over a subpoena if the stuffs bad enough. then once feds get your real IP, your internet service provider will bail you out in a heartbeat. The FBI admitted to having 2 or 3 of Americas biggest internet service providers on a kinda "instant access" type deal on everyones information. They wouldnt reveal the names of the companys as it would "affect sales or trust" of customers. no shit...
Tor would be your best bet but its very slow, can be speeded up with better configurations, but as far as "safeness" of proxies, thats as best as you can get. Still not great though.
The best of the best is a VPN. I used to own one a while back. Monthly subscription or you can pay via cash for extreme anonymity. They're servers that you connect to in countries that dont legally have to keep logs of any connections or data. Not even your service provider can see what youre doing as it just shows you connecting to one source. They're ultra fast and pretty much fed proof. Even in the past when police have HAD to confiscate servers (over child porn mainly), they've found nothing as there's nothing to find.
There's a short nerdy 101 for you