Honestly, there is not a single product out there that is right for everyone. re:coil
is very popular, and works for a lot of different hair types and textures. Based on that, I think it is worth a try, but there is no guarantee that it will work for you. I have very fine hair, and I absolutely adore recoil. It's the only product that I use every single day, regardless of what other gel, conditioner, etc I use. If it doesn't work for you, you can always sell it or swap it on the Swap forum. It's a popular product, so you should be able to get rid of it fairly easily.
As for your hair type, you look like a wavy/curly mix. It definitely looks like you have some ringlets trying to come out there. With better care, I think you might see some more curls forming.