If you're still around what you want is tracphone;
https://www.tracfone.com/homePre-paid pay as you go. Aka still has "minutes" like old pre-paid plans. As long as you aren't using it to constantly browse the web it's decent. I think the data is truly unlimited. I pay about $50 a year for my Grandmother's tracphone and she uses it all of the time to lurk facebook and makes phone calls/txts all year. Never runs out of time. Sometimes she needs a re-up in 10 months and sometimes it's 15+ months.
If you want month-to-month instead of minutes like this then go to Wal-mart. They sell cheap flip-phones with decent screen and basic web browser for about $45-$50. Then the monthly fee is $15 or $25. Can't remember exactly. I bought one a few years ago for a vacation and kept it activated for a few months. But then I decided I didn't want it anymore. I was going to re-activate it a few months back but the battery in the phone is dead and I don't feel like finding a replacement.
Note you can't get a true burner at Wal-Mart. If you want a real burner phone+SIM card like the drug dealers go to the Mexican run grocery stores/gas stations. They all sell flip phones, sim cards and pre-paid cards for cheap. Most of them will turn off the cameras or you can run the purchase through the owner's name by request. Since the vast majority of people buying them are drug dealers and illegals. So they understand not wanting your name/ID attached to the phone number.