No, you don't need a "plan" unless you do use a lot of data. There are plenty of pay as you go services that offer data. And yes data is generally cheaper for text communication than texts, so sticking to Facebook Messenger (or Google Hangouts) is a good idea. Everyone I know uses it except my parents.
P'Tel, Ting, and Airvoice are good places to start if you want a good chance at keeping your existing phone. Ting is a Sprint MVNO so it will work on CDMA networks (generally broader coverage into rural areas vs GSM only services). Check coverage before you try of course.
Google FI is a another Sprint MVNO that's a better option than Ting if you think you'll use 1GB of data a month since you get unlimited talk/text as well. If not, Ting is cheaper. Only problem with FI is limited phone compatibility, although that's not really a problem since something like the Moto G6 which will last you years only retails for ~$200.