Carrier

That means you can use it with different carriers -> your own choice.

That depends on where you purchases the iPhone, tell that you want to buy an unlocked iPhone.

When you buy from Apple Store or an Apple Authorized Reseller tell them that you want to buy an unlocked iPhone.

With some carriers there are often offers, you should not do that because you have (I think) 2 years obligations with them.

Yes, if you buy an unlock/ SIM free iPhone.

Choose your own carrier that suits you.

My iPhones (all purchased from Apple) are all unlocked, I can use at home with a carrier of my choice, and when I go abroad I can use a local postpaid and/or prepaid card.

"connect on your own later"

That means you plan on choosing a carrier later on, see: https://www.apple.com/iphone/buy/

You are essentially buying an unlocked iPhone.

You can use another carrier, see this Apple article: How to unlock your iPhone for use with a different carrier

https://support.apple.com/en-us/HT201328

But this does not mean that the iPhone is SIM free.

You must make it clear that you want to purchase a SIM-free iPhone.

Contact Apple in your region, see: Contact Apple for support and service

https://support.apple.com/en-us/HT201232

OR call an Apple Authorized Reseller in you region.