Here in the UK we have two main TV suppliers, both digital, (Satellite or cable), as analog TV has now ceased.
Both suppliers, Sky and Virgin, offer the normal range of non-3D channels, but so far only Sky offers 3D channels, for some sport and some movies.
If a subscriber has Sky then they also need to subscribe to Sky's 3D option. Whether or not that needs a special box I can't say. But we cannot watch 3D TV here in the UK without subscribing to Sky's service.
That might be different where you live, but no 3D tv will convert ordinary non-3D programs to 3D. The programs must be televised in 3D before a 3D capable tv can show it.
So, who do you get your normal TV channels from, the source, and do they offer 3D content?