Backup cameras are frequently packaged with navigation systems (the nav system provides the necessary screen for the camera), so you have many choices among cars that offer those features.
If by "distance control" you meant audible warnings when you are close to hitting another vehicle or object, you will have fewer choices. And if you were referring to adaptive cruise control, which maintains a set distance from vehicles in front of you, then most of your choices will be in luxury brands, such as Audi, Infiniti and Lexus, putting you into high-priced territory.
One exception is the Toyota Prius Five, which is available with radar-based adaptive cruise control, navigation and a parking assist feature in a package that raises the suggested retail price to $35,120 (including destination). That isn't cheap, but it's less than what you'll find at luxury brands.
Other models that meet at least some of your requirements are the Buick Verano and Ford Focus. The Verano can be equipped with a camera, rear sensors and navigation, and the Focus offers navigation, camera and a self-parking feature. If you're primarily interested in navigation and a rear camera, most camera systems include visual and/or audible warnings that alert you when it's time to stop.
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