The Apple Watch Series 3 requires an iPhone 6 or later running iOS 11. Which means it will work with an iPhone SE as long as its updated to iOS 11.
Apple Watch Series 3 - Apple
Apple Watch Series 3 (GPS + Cellular) requires an iPhone 6 or later with iOS 11 or later. Apple Watch and iPhone service provider must be the same. Not available with all service providers. Roaming is not available outside your carrier network coverage area. Wireless service plan required for cellular service. Contact your service provider for more details. Check www.apple.com/watch/cellular for participating wireless carriers and eligibility.
The watch requires a paired iPhone to setup and install apps. You cannot download apps directly on the Watch. You need to use the Watch App on the iPhone to download and install Apps.