Get a cheap flip phone or something similar without a data plan.
Also get a used smartphone and don't activate it. It'll be a personal media device ONLY, nothing else. Connectivity over WiFi only. No phone calls, which is where the cheap flip phone comes in.
If you want just one device that can do calendar syncing via WiFi and also make cell network calls, then your only option is to go prepaid. Page Plus will let you activate a Verizon smartphone and you don't even have to pay for data if you don't want to. There are several plans - $30/mo for 1200 minutes, 3000 text, 100 MB mobile data. $12/mo for 250 minutes, 250 text, 10 MB data. Or you can pay by the minute (5-10c/min) and not pay for data at all.
Hypothetically, any AT&T or T-Mobile prepaid provider should allow you to use a compatible smartphone and just insert a sim card with whatever plan you want. If you go with a contract plan with those carriers, they can detect that you're on a smartphone and will add a data plan to your service without even asking you. But if you're prepaid, they won't do that.