**ESRI.ST_Geometry:**

To my surprise, I **was** able to use the [Create Spatial Type][1] tool to create st_geometry in an Oracle XE database. This worked, despite the fact that my database was not a geodatabase. 

> The Create Spatial Type tool adds or upgrades the ST_Geometry SQL
> type, subtypes, and functions to an Oracle or PostgreSQL database.
> This allows you to use the ST_Geometry SQL type to store geometries in
> a database that does not contain a geodatabase. This tool also can be
> used to upgrade an existing ST_Geometry installation in an Oracle or
> PostgreSQL database.

-------------

**Geodatabase:**

Unfortunately, I was **not** able to create a geodatabase in the database. I believe the only way to create a geodatabase in an Oracle database is to use the [Enable Enterprise Geodatabase][2] tool. One of the parameters of the tool is `authorization_file`, which of course, I don't have, because I have not purchased ArcGIS Server.

> Provide the path and file name of the keycodes file that was created
> when you authorized ArcGIS for Server Enterprise. This file is in the
> **\\Program Files\ESRI\License<release#>\sysgen folder on Windows and
> /arcgis/server/framework/runtime/.wine/drive_c/Program
> Files/ESRI/License<release#>/sysgen** directory on Linux. If you have
> not already done so, authorize ArcGIS for Server to create this file.

As a result, I do **not** have extended geodatabase functionality in my database, such as domains, subtypes, topology, etc..

--------------------

**ArcGIS Server/Enterprise Geodatabase/EDN:**

With regards to purchasing a license for home use that would include ArcGIS Server, I think @PolyGeo was probably on to some thing with the [Esri Developer Network][3] (EDN) subscription:

> ...your most cost effective (but
> still very expensive, for personal budgets) option may be the EDN.

However, like @PolyGeo suggested, the EDN license is cost prohibitive for personal budgets:

 - EDN costs between $2,500-$6,000 + tax (Canadian Dollar), depending on the options required (date: 2017). 
 - The main options to consider are if a license of ArcGIS Desktop is required and if so which one: Basic, Standard and Advanced. In my case, I could have used the [ArcGIS Desktop Advanced - Personal Use license][4] (which is quite reasonably priced), and therefore the lower price would have applied.
 - Annual subscription (must be paid yearly), it is for development purposes only, and is for one named user.  
 - There is no home or personal use pricing option.



  [1]: http://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/create-spatial-type.htm
  [2]: http://desktop.arcgis.com/en/arcmap/10.3/tools/data-management-toolbox/enable-enterprise-geodatabase.htm
  [3]: http://www.esri.com/software/arcgis/edn/
  [4]: http://www.esri.com/software/arcgis/arcgis-for-personal-use