If you are currently not working my first suggestion is to study both the frameworks and get a good grasp of those. If you didn't get confident with Django in the first place you should reconsider going back and study more. Get a video course with some code-along and produce some simple application you can showcase on your interviews. If you already took a course take a different one. Another trainer could be more effective and you could experience something new with different excercises. There are lots of both free and paid courses out there. When you will get confident with Django get your feet wet with Node.js because it surely worth it. Node is very different from Django from some perspective, it looks more like an asynchronous version of Flask to me. Be sure to have a good knowledge of ES6 first, because it will be really useful to understand the Node best practices. Study as much as you can now if you are not working. It will supercharge you for the future...

You can easily start with SQlite. Really easy to startup since it doesn't require you to install any additional software since is self-contained. It has interfaces in almost any language and also GUIs. Start learning SQL basics and simpler data models and structures. There are many tutorials, also available in the official website. From there you will easily migrate to another database. MySQL could be next, sonce it's easier to learn at first and has more resources available. PostgreSQL is less widespread, more challenging and has the fewer resorces, but once you have some experience with MySQL is really easy to learn as well. All these technologies are really widespread and used accross the industry so you won't make a wrong decision with any of these.
This was a very reassuring take and I appreciated reading it. One of my biggest concerns (something that Stephen mentioned) is that SQLite might be too simplified to translate into a broader operational experience, but your suggestion of starting somewhere (and somewhere simple) was definitely helpful when deciding how to invest my time.
With PostgreSQL you could easily integrate JSON or array type columns and develope a simple interface to add columns on your application. Anyway handling all the data this way will require some intermediate skill with PostgreSQL dialect and a mix and match of syntaxes for your analitical queryes. Also you will need to have a good design for you backend to handle all this. MongoDB will handle all this in a more natural way and I believe will be more easily integrated with a Node.js backend.
Thanks for the response. Analytics is definitely a big part of this project and I would agree that Mongo would probably handle it more naturally than Postgres. My backend is a 3-tier Java Spring REST API, but I'm toying with the idea of using GraphQL for managing the more dynamic data coming from Mongo.
They are both fine and you will probably work with both, and many more, during your work career. So there isn't really a preferred one. I would suggest you start with Mongo just because they have a really good learning websites where you find many courses. You can use their cloud trial database to power your first applications for a fast setup. If you plan to be a backend engineer you will also need a solid grasp of SQL and Relational Databases like PostgreSQL too, so make plans to learn that too.