"get wifi" technically means just a wireless network connection. If you want internet on that, you simply need to get internet access and connect it to a wifi router....
1- Dialup: Phone line (SLOW)
2- DSL: Phone line
3- Cable: Cable line
4- Fiber: Fiber lines (Limited areas where you can actually get this, expensive, very fast)
5- Wimax: Wireless into the house: limited areas where it is used, slow, expensive. (Rural areas mostly)
6- Satellite: Expensive, slow, used in rural areas
Therefore, if you do not want cable or phone at ALL, you have limited slow or expensive options, that may not even be available where you are. If you are willing to use a phone or cable line, just get DSL or cable internet and do not buy the cable TV or phone service along with it. In my experience, cable is usually faster for the same price, though this is highly location dependent and anecdotal.