I'm back home, safe and sound, and the replacement iPhone was waiting for me. Only problem was that they still come preloaded with an old version of IOS, so my initial attempt to use the iCloud backup failed.

The steps for me (T-Mobile) were:

Go to my T-Mobile to reactivate my phone number which had been turned off just after my loss.
Open box
Get SIM number off the card. (how can Apple, with all their design wizardry make you stick a paper clip into your phone to eject the SIM, but I digress)
Enter the new SIM number online via my T-Mobile
Turn on phone and follow steps
Attempt to setup using the iCloud backup.
Fail, since the backups were from a newer version of the software.
Frantic Googling ensued.
Set up phone as a new phone
Download the software update.
Go into settings and wipe the phone
Set up again, this time choosing the iCloud backup.

From there on it was smooth sailing, all the apps came over as did my all my contacts including those flagged as favorites. I haven't checked them all, but so far only one has asked me to reenter the acct/password. The only other thing I needed to do was to set up the fingerprint recognition and reenter my email passwords.

I even got back all my photos except the few I'd taken the day of the theft after the last synch.

Only thing left to do is to schlep to the Apple store to buy a new case.

Overall, a happy camper.