Don't think you can go wrong with MySQL or postgresql. python+postgres is VERY well supported stack and can do almost anything. Great visualization and administrative tools for both. There are some data-mismatch problems, however.. node.js/python with mongodb is a bit more modern and makes it trivial to "serialize" data with sprinklings of indexes. If you're using go-lang, then RocksDB is a great high-performance data-modeling base (it's not relational how-ever) It's more like a building-block for key-value store. But it's ACID so you CAN build relational systems on top. I've used LevelDB for other projects (Java/C) (similar architecture and works great on android - chrome uses it for it's metadata-storage). Rock/Level can achieve multi-million writes on cheap hardware thanks to it's trade-offs.
I'm very familiar with SQLite.. Personally my least favorite, but it's the most portable database format, and it does support ACID.. I have many gripes, but biggest issue is parallel access (you really need a single process/thread to own the data-model, then use IPC to communicate with your process/thread).. (same could be said for LevelDB, but that's so efficient, it's almost never an issue).
If your'e using Java, then JavaDB/DerbyDB/HSQLDB are EXCELLENT systems.. highly multi-threaded, good stand-alone tools. (embedded or TCP-connected). Perfect for unit-tests. Can use simple dumb portable formats (e.g. text-file containing only inserts) all the way to classic journaled binary B-tree formats to pure-in-memory. Java has a lot of overhead, so this is only really viable if you're already using Java in your project.
For high performance "memsql" is mysql API to a hybrid in-memory index + on-disk column-database (feels like classic SQL to you though). Falls into the mysql-swiss-army-knife tool-kit.
Similarly with in-memory there is "redis".. Absolutely a joy to work with. It too is a specialty swiss army knife. Steer clear of redis for primary data that you can't lose.. while redis does support persisting data, it isn't very efficient and will become the bottleneck. redis is great for micro-queue's, topics, stat-aggregators, message-repositories (password-management systems, where writes are rare so persistance is viable). Plus I love that redis uses a pure-text protocol so I can netcat or telnet directly into it and do stuff.
I've loved cloud-data-stores.. Amazon "DynamoDB" or Google BigTable are awesome!!! Cheap compared to normal hosting fees of an AWS EC2 instance.. You can play all day.. put a terabyte up, then blow it away.. pay for what you play with. It's a very very different data-model though.. They give you a very very few set of tricks that let you do complex data-modeling - and you have to be clever and have enough foresight to not block yourself into a hole (or have customer abuse expensive queries).
Then there's Cassandra/Hadoop (HBase). These are petabyte scale databases (technically so is Dynamo/BigTable). They're incredibly efficient at what they do. And they have a lot of plugins to do almost anything you need. I personally love these the best (and RocksDB/LevelDB are like their infant children offspring). You can run these on your laptop (unlike Amazon/Google engines above). But their discipline is very different than all the other's above.