Order phone through iPhone upgrade - switch carriers at same time?

I did a search for this, but nothing popped up I found that was super recent, or that informative (so I probably missed something, apologies for that). I've been in the iPhone upgrade program for a few years, and intend to keep doing that. I would love to switch from AT&T (which is useless at my house) to Verizon and keep my number, AND order the new phone through the upgrade program when it comes out. Is that something that I can do? Or do I need to order the new phone first and THEN switch carriers/port my number? What's the best way currently to go about this?