Can my wife who is in the U.S. on an O1 visa apply to get a work permit, what are the procedures

Your wife should be able to get an Employment Authorization Document (EAD) that would allow her to work in the USA while the application for permanent residency is pending. When the application for permanent residency is granted, she wil be authorized to work based on the green card. If you wished to avoid permanent residency, you would need to withdraw the application before it is approved, but her EAD would lose validity when your application is withdrawn.
She could apply to change her nonimmigrant status from O-3 to F-1 while in the country so long as she is maintaining her O-3 status.

You mention that your two options are: "a green card application which should be easy following my O1 application, or taking a 9 month college course followed by an OPT scheme."
On what basis are you filing the green card application? Do you have an approved Labor Certificate and I-140? Or if you go back to school, you need to change status to that of a student, do the OPT and file a sponsor for the H1B, who then will hopefully sponsor you with the Labor Certificate, I-140 and then when the visa numbers are current you can adjust status to that of legal permanent resident.
Under any of these routes, your wife can obtain a work card once you are at the point of filing the resident application, not before.
You can file for an F1 while in the country as long as a school issues you an I-20. However you will not be able to travel out side the country with the Form 797 approval notice, you would have to go home first to have the student visa put into you passport at the consulate.
Good luck.