Can I pair an Apple Watch 3 series with my iPhone SE?

Yes.

Set up your  Watch -

https://support.apple.com/en-us/HT204505

M1 Mac mini, macOS 12; Watch, series 5 GPS/cellular, watchOS 8; iPad Pro 2nd Gen, iPadOS 15; iPad Air 2, iPadOS 15; iPhone 12 Pro, iOS 15; TV 4th Gen, tvOS 15  HomePods, audioOS 15 and Airport Express w/ Airplay 2