Question: What size of image I need to have if I want to use it as background to full screen?

1.png 320 - 568 points non retina

1@2x.png 640 - 1126 points retina

Am I right? Or what size are correct?

Answer: 
You could use the size of the splash screen images for your views too, making your app iOS 7 forward compatible.

For iPhone 5 and iPod touch (5th generation):

640 x 1136 pixels

For other iPhone and iPod touch devices:

640 x 960 pixels (retina)

320 x 480 pixels (standard resolution)
It depends on what device you're targeting. If you looking at just the iPhone 5/5s then you're spot on. If you're also taking into account everything below the iPhone 5, then you will also need

320x480 (non retina)
640x960 (retina)

So it just depends on the devices you're supporting. There are loads of resources on the net about these things. Also bear in mind that the background size will be different depending on what components you use, such as navigation bars and tab bars. And also if you're supporting iOS 7 then the status bar is transparent, where as on iOS 6 and below, you don't need to provide the background for that (so the above dimensions are actually correct for iOS 7 but not exactly right for iOS 6)