An iPhone 4 or above will work. Here are the iOSes that apple phones (4 and up) will go up to:
iPhone 4- up to iOS 7.1.2
iPhone 4S - up to iOS 9.3.5
iPhone 5 - up to iOS 10.3.3
iPhone 5c - up to iOS 10.3.3
iPhone 5S and up - iOS 11 (latest)
Please note Apple also has released the iPhone 6, 6s, 6 and 6s plus, 7 and 7 plus, 8 and 8 plus, and the iPhone X. Not to confuse you, be very careful and considerate when making the decision. The iPhone X has no home button, exits apps by swiping up.