One thing I thought of is this: All points leading to me go through my ISP, so is there anything I can do to secure/anonymize myself between me and my local ISP? I had thought that a VPN would help in that way, which is why I began by asking about that. Yes, I think I want web browsing anonymity. Let's start with AT&T. Can I do this? Can I go farther?
Short answer: No. Long answer: what JBI said, plus more. Look at it this way. Though it may not be physically, logically your connection to your ISP is dedicated to you. Any traffic over that link is identifiable as you. The target address and port of that traffic is known. It must be in order for the network to route the traffic. You can't hide that. Something like Tor will obfuscate it by routing traffic through all sorts of middle men. Https will encrypt the data being transferred, but the end points are still known. For example, I can tell that you went to the google search page, but not what you searched for. Even with https, you can leak important data. The initial url in the https request will be sent in the clear and it arguments are passed in that url, they are readable even though the remainder of the session encrypted.
If you don't want your ISP to be able to see your traffic, then you need to have a VPN server somewhere out in the cloud that you can connect to from your home network and route all your traffic over. This obviously costs money, and whoever is terminating your VPN connection can still snoop all the packets coming out as they leave the machine. You've simply changed to entity that provides the first hop out of your network from your ISP to you VPN host.
With Tor, you cannot use it for anonymous and non-anonymous browsing. In other words, you can't even sign in to a sight that has identifying information on you. As soon as you do, the anonimity that Tor provides falls away, at least for an organization with enough resources to watch traffic coming out of a large number of Tor exit nodes.