hide IP addresses. It establishes a virtual encrypted tunnel between a particular network and host across public networks in essence virtualizing a connection as if you were local to the private network in question.
There are proxy services out there which can provide such functionality up to a point but there is always a trail. Always.
The paranoia isn't worth the money.
If you want to be completely impervious you need to purchase multiple devices in bulk, use and lose,, and access whatever it is you deem sensitive via free wifi networks. That way you're still randomizing IP addresses as per whatever is available in the DHCP pool in question.
Nevertheless there will always be a unique physical MAC address associated with any device, and yes, there are utilities you can use to "mask," that, but the bottom line is, there are forensic utilities which will even uncover that.
So...Go the anon, disposable route, which works well for superspys and terrorists, or...ratchet down the paranoia and be smart
For laptops/PCs either of the following:
Tor browser: https://www.torproject.org/
Tails OS: https://tails.boum.org/ (can run this from a USB or as a virtual machine)
Pat J