Help MY IPHONE ISN't WORKING?

Okay, i have a iphone 5s (bought in march) and i updated it to IOS 9 when it restarted it stayed on the sane screen until it died (20 mins) and now when i charge it it srays on the reset/restart screen Please Help!

Added (1). *same

Added (2). *stays

Added (3). Yes thank you guys but the problem is that its ALWAYS on the reset screen (the one with the logo)

Should I buy the iPhone 6 or 6s, and it what color?

So IIm saving up a bunch of money for a new phone because my phone is a Samsung and IIm not an android fan because before that phone, I used the iPod 5 for about 3 years and IIm so used to iOS. Also the iPhone 6s is $650 where the iPhone 6 is $550, and both are unlocked and 16Gb and brand new, but IIm only 15 and it's hard for me to get cash quickly, and no way in hell would my parents even consider buying me a $650 dollar phone, let alone a $200 dollar phone. And IIm still trying to choose between gold, space gray, or rose gold.