Can I get an Apple Watch without having an iPhone at all

No.

The Apple Watch is an iPhone accessory. The iPhone is required.

You will need an iPhone 6s, SE (1 or 2), 7 or newer, running iOS 13 or newer.

No. You need to use your iPhone to sign up your Apple Watch Device. However, if you buy an eSIM for your watch, you can use your watch without an iPhone. Actually, you can buy the the iPhone 6s if you don't want an iPhone but only Apple Watch. The only thing you need to let your Apple Watch be an independent device is your Apple ID and an eSIM.