Does it matter which cell phone carrier I get if I don't plan to have a SIM card?

When buying a new iPhone I see ones that are unlocked for AT&T and ones unlocked for ones like Verizon or Sprint. If I don't have an cellular plan or SIM card, does it matter which one I get if I'm planning on just using Wi-Fi Calling apps. I could get a fully unlocked one but I don't know if that matters and they are harder to find

The Verizon version is fully unlocked so that is the best one to buy. Otherwise if you don't plan on using the cellular radio you might be better saving your money and getting an iPad mini or a iPod touch.

I don't think it matters

If you buy at the Apple store they are unlocked (unless you choose some carrier financing option).