Saving an archive?

Do you remember if your stories were saved in MySQL or files?

MYSQL. I just check with PHPAdmin and my stories are there.

There are several threads around here where people have done this before so you can find more details/troubleshooting there. Typically your course of action is the following:

Back up your database if you have not yet done so.
Upload a fresh copy of eFiction, except the install folder (you won't need this).
Make a copy of config.php and fill out your site's information.
If you were running an older version of eFic you'll need to run the upgrade.
Reupload your skins if you have them.
If you had any mods/hacks of the files, you'll have to redo them.

So config would be the only file that I would need to edit?

With a clean install. If you've modded your site at all then you'll have to redo those mods.

I haven't done this in a while so I could be leaving something out; it's best to do a search for some of the other threads where people talk about this.

Had you done any changes ("mods") to the files since your "month old" backup?  If you haven't, those should still be good.  Any day-to-day changes (adding stories, reviews, memebrs, etc.) should have been saved (and safe) in your MySQL database.