A VPN will protect you from your ISP, your router, or any public network you connect to knowing which specific domains you go to. (HTTPS protects the rest, so without a VPN they might be able to see you visit socialmedia.com but not socialmedia.com/thisspecificperson/thisspecificpost, and with a VPN, all of your traffic would just look like your computer > VPN company)
A VPN won't protect you from the places you visit online fingerprinting you with anything other than your IP address. If a site can see your screen size, installed extensions and fonts, what graphics capabilities your computer has, the username of your account, your typing style, browser version and type, etc, it's not gonna be hard to figure out that you're the same person whether or not your VPN is on.
Use a VPN if you don't trust your current network, or your internet service provider to not log what domains you go to. (or to circumvent region-blocked content by connecting to a server in that region) Don't use a VPN if that doesn't matter to you. Everything else about your privacy will likely remain identical otherwise.