So got a few more questions:
1. Do we need to pay for an IHS surcharge or is this included in the application fee?
I thought it's separate but I couldn't see anything around that during the online application
There is no IHS surcharge for a fiance visa - if you were supposed to pay it, it would have been part of the online application submission.
People on fiance visas are not entitled to use the NHS for 'free', so they do not pay the IHS. Instead she has to take out health insurance and pay for any and all medical treatment in the UK.
If she does not take out insurance, she will be charged 150% of the full cost of the treatment (not the NHS subsidised cost).
2. We've booked an appointment at VFS Premium Application Center - Chicago 564 West Randolph Street. How and when do we pay for the priority processing? It said on the online application that there's a "Premium Service" but from what I gathered that's no applicable for a Settlement Marriage Visa. Is the Premium Service different than the "Priority processing"
There is no premium service for settlement visas and you should not have been able to book an appointment at a VFS Premium Application Centre, since you are not eligible to apply that way.
You have to attend biometrics at a USCIS Application Support Center. The biometrics are taken by US immigration on behalf of UKVI and then you mail the application and documents to Sheffield for processing.
There is only one office in Chicago where you can give biometrics:
USCIS Application Support Center
5160 South Pulaski Road Suite 101,
Located next to Super Mall Chicago, IL 60632-4253.
Chicago, IL.
You should have been prompted to book the biometrics appointment at this office (or another office in Illinois) as part of the online application.
Priority processing is a service offered by UKVI Sheffield, where they put your documents to the front of the line when they arrive in Sheffield. You go to the VFS Global website, purchase priority processing for $771, print the receipt, put it with your documents and write SETTLEMENT PRIORITY SERVICE in large letters on the very outside of the package.
3. How does the shipping work? Is it done through VFS? Is that the most straightforward?
You can either ship it yourself with UPS or DHL (and then include an online account number so your account can be charged for the return shipping), or purchase pre-paid UPS shipping labels through VFS Global.
If you purchase through VFS, you'll want to pay for both priority processing and the shipping labels in the same transaction.