I use the AT&T Go Phone, I believe it's now called AT&T Prepaid Phone. Here's the phone, it sells for about $25 but between Walmart, Target and Walgreens you can find one of them usually has it on sale for $9.99. That's what I paid at Walgreens last year. I'm on my second one, the first phone the battery died after about 4 years, it's cheaper to buy a new phone than a battery.
I go to their website and have set up an account page, and once a year I buy a 1000 minutes for $100. That's it, one time fee, and the minutes even roll over. I could buy less but then you wouldn't get 12 months, and I don't want to be bothered buying minutes every 3 or 6 months. The phone service is good.
The first time you'll probably want to call them to establish the phone number, your account and they will mail you a sim card. Here's their website;
AT&T PREPAID - Prepaid Phones, Tablets & Plans