I highly recommend the sgp glas screen protectors. I had one on my iphone 5 and you get no rainbow scratches... And the screen looks like the naked iphone screen. It is made of glass. It can pick up very faint scratches (i don't know how as im careful) but way less then plastic, but you cannot see them at all whilst using the iphone - def no rainbow.
I got no bubbles and it stuck down fully on all edges (it uses adhesive but removable) and it doesn't ever peel up at the corners. They are expensive but i wouldn't buy anything else. The plastic ones are crap no matter what brand.
I had to replace my iphone 5 cos it got run over by a car (fell out of pocket in road)!! So ill be buying the new thinner version of the glas as soon as it comes out.. But the previous version with rounded edges was brilliant anyway - i might not wait...
http://www.spigen.com/brands/apple/iphone/iphone-5s.html