Phones like the Iphone?

[Ello Aspen!]

I want to get a phone that is similar to the Iphone 4s or Iphone5. I really like the text conversation speech bubbles that keep it so organized. And its really important for it to be able to go on the internet and have apps like Instagram and stuff. Plus I really like the shape of the Iphone, where its thick and has a square kind of shape and gets lots of nice cases.
Is there any kinds of phones that are kind of like that or fit a few of those descriptions? I would just get an Iphone but they're too expensive to buy without a contract. My parents will really only go for a phone that has a pay as you go plan or something, but they refuse to get a contract. My last phone got water damage and was just a crappy Wal-mart $50 phone.
Thanks to anyone who understood this stupid question and can give me a good answer or opinion on a phone.