I have an old iPhone 3gs (it's not broken, so I don't 'fix' it) and switched to Ting, and just bought a full price Kyocera dumbphone for 80$ as my normal text/call phone. I kept my iPhone and still use it for music, email, etc., and I have wifi at home and work so it basically functions as it always did.
When I had data turned off on Ting, I got iMessages on my iPhone while I was on Wifi, and since most of my family has iPhones, most everyone went through iMessage. For people without iPhones, their texts came in on my dumbphone like usual. When I wasn't in wifi, messages sent as a text on other iPhones sometimes didn't reach me at all on either phone, especially pictures and videos.
I ended up turning data on in Ting, which now redirects all texts to my dumbphone, but now I never miss a message. Last month they didn't bill me at all for my data usage, since I used so little (1 Mb on the 100Mb 'plan'), so that's a win. My texts have gone up since none are free anymore, since they're not iMessages.
This has been a very good route for me and I'm happy with it - it's a 23$ phone bill over 80$ at AT&T or 56$ at Tmobile, with a dumbphone for phone usage and my iPhone as my fun toy.