How do you create a new database with new sid on Oracle's pre-built 11g virtual machine?
Are you sure that your Developer Days VM 2016-06-02_13 runs Oracle 11g?  I'm using the same, and it reports: 

SQL&gt; select * from v$version;

BANNER                                                                               CON_ID
-------------------------------------------------------------------------------- ----------
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production              0
PL/SQL Release 12.1.0.2.0 - Production                                                    0
CORE    12.1.0.2.0  Production                                                                  0
TNS for Linux: Version 12.1.0.2.0 - Production                                            0
NLSRTL Version 12.1.0.2.0 - Production                                                    0


Reading your questions/explanations, I cannot tell how familiar you are with 12c's "multitenant option", which "allows a single container database (CDB) to host multiple separate pluggable databases (PDB)" (see eg oracle-base.com).  For starters, a new PDB may be just what you need ... an overview of Oracle Multitenant can be found here.

In this article, section "Where to get started", you can see that the SERVICE NAME (not the SID) is used for connecting to a PDB.  More about PDBs (cloning etc), with screen shots, can be found here.  SQLDeveloper (already installed on the Developer Days VM) is probably the best tool for getting started.  I'm not aware of any "wizards" that one could use.

Using Java: When connecting to a PBD, using a JDBC driver, make sure that you use the service name (again: not the SID). 

SID (for connections): it seems that the SID is only used for connecting to CDBs (not PDBs) nowadays.  Although - I have also used the "service name" successfully for accessing CDBs.