Add to the fact that no matter if you use a dynamic IP, anonymous proxies, or whatever else, remember that Google saves practically everything ever searched from every IP address that ever connected to their site and used their services.
Wrap your head around that.
Additionally, a lot of other search engines use google for their own searches, so even if you want to stay away from google's "eyes", you still have to find a search engine that doesn't use them at all.
Just keep in mind, that if you look / search for child porn, instructions to build h-bombs, or how to kill the president, there's always a slight chance that the government will be able to figure out who you are, no matter how careful you are.
If you're extremely worried, and have some brains to spare, you could hack into other systems and use their internet for your nasty internet uses, or use "IP Spoofing methods".
In short,
How to hide IP address and use internet safely?
isn't necessary unless you're trying to do something extremely illegal. Just don't do it and you won't get caught.