The cheap compact camera market is a deluded with me-too offerings. However, the best cheap compact cameras can be found by looking at which higher- end camera models have come down in price.

Features to look for: zoom lenghth, maximum aperture size, wifi, GPS, touchscreen, image clicking time, Full HD 1080p video recording i

Go for the quality: Ask about sharp, detailed images, abke to keep noise (blotches that happen at higher ISO settings) out, fast focussing time, minimal delay between pressing the shutter button and the capturing of the photo.

The best cheap compact camera: Canon PowerShot ELPH 350 HS
The second best cheap compact camera: Nikon COOLPIX S6900 (great for selfies using the touchscreen)
The cheap compact camera with best battery life: Samsung WB350F (also has great zoom quality)