Ping is usually tied to distance. I'm on the west coast of the USA. If I connect to servers in LA, SF, or other such close places my ping is fine. If I connect to east coast servers my ping is usually double. If I connect to UK servers I'm usually at least 4x what my normal servers all. My net connection never changed, just the location of the server I connect to.
That being said some of your problems has to do with the 6MB down. You could do with faster, more so if you are sharing that connection. I gamed ok while on DSL, but if anyone else was using it then I had issues. I have issues with my current Cable connection because I have three 4K TVs, 5 cell phones, and other gaming devices on it. So if everyone is home, family of...