My research group shares a server for which I do not have root access. I would like to install a database in my home directory to manage my results. What would the best option in terms of ease of install, features etc? I read Installing MySQL without root access but I think a full mysql install seems like overkill. Is SQLite a good option? I've never worked with it. I'd like standard SQL features with reasonable performance but I don't anticipate too many exotic needs. I can request temporary root access for installs, configs etc.
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Why don't you use the system's MySQL and set up your own database which you control? You don't need to set up a clean SQL install if all you need is root access to a specific database.
Ask your sysadmin to create a new database for you and to grant your user all permissions on it.
It depends on how much data you'll be storing. If you'll only have a few dozen tables with a few thousand rows in each table, SQLite should definitely be sufficient for your needs.
SQLite isn't nearly as robust as MySQL, but for most basic needs, it's sufficient. Almost every application that I write that needs some sort of data backend uses SQLite. A lot of desktop applications nowadays use SQLite to store information (e.g. Calibre ebook manager), and it's the standard data store for Android applications.
For a comparison of features between different RDMS, you can check Wikipedia.