The coordinate reference system is longitude/latitude and theWGS84 datum.
The "geopackage" format is the a very good general spatial data file format (for vector data). It is based on the SpatiaLite format, and can be read by software using GDAL/OGR, including QGIS and ArcMap.
A "R SpatialPolygonsDataFrame" (.rds) file can be used in R. To use it, first load the sp package using library(sp) and then use readRDS("filename.rds") (obviously replacing "filename.rds" with the actual filename). See the CRAN spatial task view. Note that this is different R file format than used in previous versions (the RData format that could be read via 'load').
An "ESRI file geodatabase" is the standard format used by ArcGIS.
A "Google Earth .kmz" file can be opened in Google Earth.
A "shapefile" consist of at least four actual files (.shp, .shx, .dbf, .prj). This is a commonly used format that can be directly used in Arc-anything, DIVA-GIS, and many other programs. Unfortunately, many of the non standard latin (roman / english) characters are lost in the shapefile, so you should avoid using it. If you insist, you can use the .csv file that comes with the shapefiles, or the attribute data in the geodatabase for the correct attributes (the geodatabase is a MS Access database that (on windows) can be accessed via ODBC).
An "ESRI personal geodatabase" is a MS Access file that can be opened in ArcGIS. One of its advantages, compared to a shapefile, is that it can store non-latin characters (e.g. Cyrillic and Chinese characters). You can also query the (attribute) data in Access or via ODBC.
Some files have been compressed and grouped in ZIP files. You can use programs such as 7-zip to decompress and ungroup these files. This dataset is freely available for academic use and other non-commercial use. Redistribution, or commercial use is not allowed without prior permission.