Aye, that's the rub. Data on the cellular network can run up the tab quickly, especially with a phone that does everything over the web.
You can buy a older Gingerbread Android phone for under $50 with some careful shopping. Don't register it with Google, for the sake of privacy.
Stuff in a prepaid SIM. Lycamobile is 2 cents per minute, 5 cents per megabyte, and your prepaid time never expires as long as you use the phone at least once every 90 days. I'm sure there are others with similar rates, or ones that work better for you.
Make sure you turn off data when you're not using it, because Android always likes to phone home (even when unregistered) and will run up your bill if allowed to.
If you install all local apps (calendar, maps, and so on) rather than using Google's online services, you not only get better privacy, you also get much lower data costs. You have to hunt these apps down - with an unregistered phone, you're side loading everything - but you'd be surprised how much is out there that's FOSS, private, and quite good.
I'm glad to see this phone as an option. However, I don't think it offers that much value at the low end, and I'm not at all sure it gives you the same privacy you have with an unregistered Android phone. I could be wrong.