The very short answer is it depends if you are content with an integer (Long) or want decimals (Double). After that, it depends if you're concerned with storage size, in which case choose the smallest data type that suits your needs.
beyond the video, you should really know something about data and its representation in tabular form. The information here
provides guidelines as to the types of fields you can have in tables and what you can expect as acceptable data for such fields.
Barring that, experimentation would be illustrative as well.
Kudos to Darren who snagged first
Also if you work with Geodatabase Feature Class instead of Shapefiles, the geometry metrics is mainteined, i.e., the Shape Length and Area fields are added and calculated automatically (the units would be same as the unit of the defined projection system of the Feature Class).
In case of a shapefile, you need to update it using Calculate Geometry every time you want to see these attribute after making changes in the geometry of the shapefile.