There are several IOT services out there to which you could send your sensor data - for example see the list here https://iotdb.org/social/imadeit/post/95279811682/iot-datastore-roundup - to which the MySensors cloud service will one way be added perhaps.
If you want to run your own, one question is whether you want to retain all data forever, or just a rolling buffer of more recent data. For the latter, something like RRDtool might be more efficient of time and space then a relational database. For full generality a relational database would work, but do calculate how big it's going to get and think of your usage patterns - do you need arbitrary queries?
Using something like MQTT might be helpful as an intermediary between the sensor network and a database or datastore; it could also make it possible to run both Home Automation and data logging from the same network. For example, if the sensor network provides a broker, both the HA software and the logging software can subscribe to the relevant topics.
