Websites using Google Analytics and various advertising networks can very well track and identify visitors based on a variety of different inputs with their browser (see browser fingerprinting). Therefore it’s best to use a VPN in conjunction with a secure browser configured for more privacy. See my guides: secure browser (an overview of different browsers) and also Firefox privacy, which deals with privacy configurations, tweaks, and add-ons.
Let's talk about what happens when you use a VPN app on your computer or mobile device. Any VPN app will require an existing network connection to be able to connect to the VPN service provider. This means that even if you set your VPN app to automatically launch when your device boots, there will be a period of time when your computer is connected to the internet directly, not through your VPN.