Hello!

My fiance & I just had our K-1 / K-2 approved. They will be arriving here around the end of November, & we will marry shortly thereafter.

My fiance will need to return to her country for a 2 month period this coming March & the following fall in order to finish her advanced education. I have read through some of the informational posts here, & I have been overwhelmed with so many posts to read through.

What do we need to do, in essence, & in what order? I am also slightly confused as to whether we should obtain their SSN's prior to the marriage or not.

Any help would be greatly appreciated!

You apply for SSN before marriage, give it a weel or so to get in the system.

After you marry, you file to adjust status and at the same time you can file for employment authorisation (EAD) and advanced parole (AP). AP allows you to get back in. Allow 3 months for AP to arrive.

And don't leave the country without the AP in hand.

Thanks!

Which name would be the best one to use for my wife...her current name, or the one she will have after we marry?

I don't see why she can not just finish her advanced degree here in the states

That's a personal choice for you two---which is 'better'. If your wife wants to change her surname, she can do so with the AOS application(s).
If her immigration documents are in her married name and her passport is still in her maiden name, remember that she will book airline tickets in the name that matches her passport. She can then carry a copy of your marriage certificate to show the name change from passport-->immigration documents (green card, AP etc).

We decided that it would be better for her to finish her degree in her native country.