The easiest one is SQLite. I once used it a bit, and using it is E-Z. It does not use a database-server process, and the database's contents are stored in a file that one points to with the SQLite software. So selecting it is essentially selecting a file to open.
However, it does not do large datasets very well, I mean datasets in the hundreds of megabytes or gigabytes. Speakpigeon, how much data do you want to store?
Relational databases store their data in tables, essentially spreadsheets with named columns. The data attributes of each column's entries are the same by column, though different columns can have different attributes. Attributes like string, integer, unique (yes, one can impose uniqueness), whatever the software supports. SQL ("Structured Query Language") is a language for manipulating the contents of these tables. Here is the W3Schools tutorial:
SQL Tutorial -- to read from a database, use the "SELECT" command. To add new data, "INSERT", to alter data, "UPDATE", and to delete data, "DELETE". There is also a lot of stuff for specifying data sources and destinations, conditions to perform some operation, etc.
There are some alternatives to relational databases, like key-value ones and hierarchical ones. Key-value databases are easy to do within relational ones, but hierarchies are more difficult. One gives every row a unique ID number, and one also gives each row a parent ID number in the hierarchy. The root node gets some special parent ID number, like 0 or -1 or NULL (blank database entry, not 0 or a zero-length string).
