What is the most appropriate version for 2 GB geodatabse created at version 10.1 ?
I suggest to use the SQL Server express that is accompanied with the ArcGIS Installation media (DVD) and stay away from newer versions of SQL Server for this purpose.
- If you downloaded the installation file from the Esri Customer Care portal, unzip the file and run the ESRI.exe.
- If you have an ISO file, use an ISO extractor to access the installation files and run the ESRI.exe.
- If you have an ArcGIS for Server Workgroup, ArcGIS for Desktop, or ArcGIS Engine DVD insert it to the appropriate drive and run the ESRI.exe.
Click Setup next to ArcSDE for Microsoft SQL Server Express to start the installation wizard
For 10.1 details requirements can be found at here
As esri staff kpeter says about comparison between ArcSDE for SQL Server Express and ArcSDE geodatabases licensed with ArcGIS Server Enterprise
Yes, you can use SQL Server Express with Enterprise. As for "...it's supposed to work fine", there are no functional limitations that ArcGIS places on it, but your performance will likely not be great because of the limitations inherent in SQL Server Express itself (maximum memory used = 1 GB, maximum use 1 socket or 4 cores, maximum database size 10 GB - http://technet.microsoft.com/en-us/library/cc645993.aspx) If you truly have a production enterprise system, then Express is not the recommended DBMS to use for your enterprise geodatabase.