At the bare minimum, all you need is a broadband connection. Any internet service that is faster than dial-up is considered broadband. Cable, DSL, and satellite are all broadband internet services. Even the lowest speed tier of DSL should be enough.
If you are experiencing latency issues, I suggest that you report this to your internet service provider and find out what they can do for you.
On the other hand, lag is more likely attributed to running the game on an older computer that doesn't meet or exceed the game's system requirements.