Part of this can't be answered without knowing what kind of performance you need out of your database. On the Raspberry Pi, you have a couple mainstream options.
- Flat files such as JSON, XML, or even just TXT.
Options 1 and 2 will both use a significant amount of resources. If properly configured, they're probably going to be the fastest databases. MySQL will use slightly less, and is configured to give the best performance for data retrieval. PostgreSQL on the other hand has support for much more complicated queries and is optimized for insertion.
Since you're on an RPi, you can probably get away with using SQLite. Like PostgreSQL and MySQL, SQLite is a relational database, but it's all stored in a single file. There is no separate server processes that consumes resources. It has all the features of the SQL spec, plus a few extras. Though it does come short of PostgreSQL's more robust feature set.
Lastly you could go with option four. If you "need" a database, flat files are probably going to be the least attractive option. They will require the most amount of work from you, but have a relative overhead of 0. I wouldn't recommend this approach for anything other than a particularly small dataset.