You don't typically buy Wi-Fi. You buy Internet access from an ISP (AT&T, Comcast, or whatever is in your area), which in turn, you buy/rent a modem that may or may not have Wi-Fi access. I don't really believe that most providers offer "cheap" service, at least not without a long-term contract. And plus, most Internet packages usually give you 1 TB (1,024 GB) of data, not just 1 GB or in some places, unlimited data.
The most likely reason that your downloads on your phone are slow through mobile data is either because you're too far from a cell tower and have a weak (and slow signal) or you've reached your monthly threshold. With "unlimited" data, almost all providers will slow you down to a crawl after you reach a certain amount of data used.