Calculating all distances from single points to multiple polygons

This is fairly simple to achieve using QGIS (I think any version will do) and a very simple SQL statement in DB manager. But for that your that must be in some kind of spatial database (Postgis or spatialite). Since it's more accessible to most people, I will assume using spatialite, but the SQL statements are the same for Postgis.

1. Create a new Spatialite database;
2. Import your point and polygons layers into the new database;
3. Open DB manager plugin, select the database and run one of the following SQL statements:

Distance from all points to all polygons boundaries

SELECT 
  f.point_id,
  g.polygon_id,
  st_distance(g.geom, f.geom) AS distance
FROM
  points_table AS f, 
  polygons_table AS g

Distance to all points to related polygons boundaries (assuming that a common field exists)

SELECT 
  f.point_id,
  g.polygon_id,
  st_distance(g.geom, f.geom) AS distance
FROM
  points_table AS f JOIN 
  polygons_table AS g ON (g.common_field = f.common_field)

Distance to all points to related polygons centroids:

SELECT 
  f.point_id,
  g.polygon_id,
  st_distance(f.geom, st_centroid(g.geom)) AS distance
FROM
  points_table AS f JOIN 
  polygons_table AS g ON (g.common_field = f.common_field)

Notice that you can add any field from your layers to the result:

SELECT 
  f.point_id,
  f.point_number,
  g.polygon_id,
  g.parcel_name,
  st_distance(f.geom, st_centroid(g.geom)) AS distance
FROM
  points_table AS f JOIN 
  polygons_table AS g ON (g.common_field = f.common_field)

Or even all fields:

SELECT 
  f.*,
  g.*,
  st_distance(f.geom, st_centroid(g.geom)) AS distance
FROM
  points_table AS f JOIN 
  polygons_table AS g ON (g.common_field = f.common_field)

The Generate Near Table tool in ArcGIS will do what you want, but it requires an Advanced license and will do it for all points/polygons - not just those associated with each other. This means for each of your 95 objects you will get the ranked distance for all 211 properties, so 20,045 rows in the table. You'd either have to filter the resulting table or as Emil suggests automate the task to create selections based on the association and only run it on those groups.

As far as filtering, yes, a join (followed by a definition query or selection) is all you'd need. The tool result gives you IN_FID and NEAR_FID. Depending on how you run the tool (properties near point, or point near property) determine which FID is which. You'd then join your point and property tables (both) to the tool result based on the appropriate FID.

This assumes each of your 211 property records has an attribute that says which of the 95 points they belong to, because the next step is to select (or definition query) all records in the joined table(s) where two fields of one record should match - point name field = property associated point name field. The cases where they don't match are polygons that aren't associated with that point, so you don't care about their distance from that point.