Ina,

I think Excel or some other spreadsheet ought to be just fine for most home
gardeners.

You need the relational system with multiple related data tables when you
have to track multiple plantings in different areas, or make multiple-year
observations on a given plant, such as bloom times, for instance. Besides
bloom times and locations in the garden and greenhouses, I track family
names (by genera) in a separate table in the main relational database. I
track suppliers' names, addresses, contact info, etc., in a separate table.

I recommend Excel or the Calc in OpenOffice (see openoffice.org).