Can I use a T-Mobile iPhone 5s on Walmart's Family Mobile, powered by T-Mobile?

I'm looking to buy an iPhone, but worried about it not working with Family Mobile, since it's not a "traditional" service (for lack of a better word). The representatives at my local Walmart say that our service can be paired with any T-Mobile phone, which I have used before, but only with androids thus far. It says that the service can work on the iPhone 5, but since the iPhone 5s is a newer model, I was wondering if it'd be the same? Also, I'm worried that my internet might not be available on it. I don't want to invest hundreds of dollars to have it not work out.