Honestly, it depends on how anonymous you really want to be.
I'd start by using a live CD/USB so there is little (if any) physical traces of data left on a machine.
Find a decent firewall, learn to configure it properly.
Always use encrypted communications (HTTPS/SSL) where possible.
TOR is alright as long as you don't mind the exit node seeing all your data.
Just keep searching online and you'll find so much information you won't know what to start with.
Also, if you want to go tinfoil-hat, look into buying a TEMPEST-approved monitor.
https://en.wikipedia.org/wiki/Tempest_(codename)