Well if you are going to use mostly WiFi you have to keep in mind that even high end routers struggle to get > 300mbit actual throughput (the speeds they write on the box are mostly fantasy) in good conditions. So you do not have to get the 1gbit package if you are just going to use WiFi (unless it is cheaper of course).
In Switzerland there are 3 main types of internet connection (excluding the wireless ones like the one @bojack mentioned):
- Telephone lines (ex. ADSL), those are offered mostly by phone companyes (Swisscom, Sunrise, Salt …). Those are usually the slowest as the medium is the most restrictive
- Coax (Cable TV), those are offered by cable companies (Cablecom, quickline …). They are quite fast and usually relatively inexpensive but they do seem very keen on bundling a TV package.
- Fiber, fiber is the fastest and is offered by the big companies and a bunch of smaller ones. Where available there are sometimes very good offers (like the one by salt offered a while back).
It is definitely worth checking if you have fiber(in Zurich you might actually be lucky) but if you are just going to use it to browse Facebook on a phone I would just get the cheapest offer >20mbit. or a good mobile plan with infinite internet from any of the providers (I know that sunrise and salt offer a 2. sim-card for a small fee so you could install an LTE router).