In case this helps other people:
PennDOT rules on what paperwork is needed can be found here. In addition, keep in mind the following:
We needed a letter from my employer, I94+passports, old licences, 2 proofs of residence (lease+bills), and a rejection letter from Social Security for the SSN (for my wife) and a letter with the number on it for me (haven’t got the physical card yet).
If you have a H1-B, and your spouse has an H4, you will need to go with your spouse if s/he is getting a licence as well - you can’t go separately.
PennDOT does not take cheques drawn on foreign banks, only US banks. Fortunately you can get money orders easily at grocery stores. There is a Giant Eagle that does this near the Penn Hills licence centre.
Staff are pleasant but extremely over-worked, so be patient. Downtown Pittsburgh was less busy during the week than Penn Hills on the weekend.