Transferring from a 12 mini to a 15 in terms of just getting your data, apps, and settings migrated is trivial thanks to the great tools Apple built into iOS. The initial setup assistant (“Hello screen”) will take you through it all — it’s a piece of cake, no special expertise required. Having a good backup on a local Mac or on iCloud in place first is best practice.
IMHO the tricky part, or rather the part you can least influence yourself, is migrating from the old nano SIM to the new eSIM. That part involves the carrier. Initially, I was expecting this is where things could get hairy. But, to my great surprise and pleasure, that went without a hitch on our T-Mobile iPhones. It just worked. Not long after following the on-screen instructions on the old and new phones, I ended up with a new iPhone 15 with perfectly working eSIM and an old iPhone 12 mini with deactivated nano SIM.
I cannot judge if on Verizon you will see the same seamless eSIM transition. Judging by how many people have to go through this and how Apple and carriers will not like to absorb a lot of cost from a huge volume of additional support calls, I would, however, take my chances now that I’ve seen that this can work perfectly.
How about you get your iPhone from whoever makes you the best offer and gets it to you quickest, and then you just start by doing it yourself following the on-screen instructions? If you then run into issues, you can always call Apple or your carrier, and if that doesn’t lead to immediate remedy, you can still take it in to one of their stores. Keep in mind, as long as you have that backup (ideally to both a Mac and iCloud), you risk almost nothing, so you could try almost anything. Good luck! 