SQLite

PhP might be old fashionned but Laravel is really great. I've tried nodeJs backend with express, python with flask and a little bit of serverless, and quite frankly, laravel was by far the best in my opinion. It has a lot of official packages that speeds up development (from authentification to serverless deployement), it also uses Eloquent ORM that support Mysql databases. Finally it works great with VueJs for the front end development.

I recommend ExpressJS or NestJS as BackEnd and React as Front-End and PostgreSQL as the database. The reason is as follows. First of all, since it is a financial system, various services will exist, and each service must be well connected and combined with each other. The organic combination of small services that work very well is the foundation of a great system. For this, it is best to use Node.js based, and I think ExpressJS or NestJS is the best choice. We recommend choosing React or Vue as the FrontEnd. PostgreSQL is currently the best performing database. These three combinations have many examples, and their superiority has been confirmed by my implementation in many projects already. If you are interested in my advice and have any questions, please feel free to contact me.

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.

A question you might want to think about is "What kind of experience do I want to gain, by using a DBMS?". If your aim is to have experience with SQL and any related libraries and frameworks for your language of choice (python, I think?), then it kind of doesn't matter too much which you pick so much. As others have said, SQLite would offer you the ability to very easily get started, and would give you a reasonably standard (if a little basic) SQL dialect to work with.

If your aim is actually to have a bit of "operational" experience, in terms of things like what command line tools might be available as standard for the DBMS, understanding how the DBMS handles multiple databases, when to use multiple schemas vs multiple databases, some basic privilege management etc. Then I would recommend PostgreSQL. SQLite's simplicity actually avoids most of these experiences, which is not helpful to you if that is what you hope to learn. MySQL has a few "quirks" to how it manages things like multiple databases, which may lead you to making less good decisions if you tried to take your experience over to different DBMS, especially in bigger enterprise roles. PostgreSQL is kind of a happy middle ground here, with the ability to start PostgreSQL servers via docker or docker-compose making the actual day-to-day management pretty easy, while still giving you experience of the kinds of considerations I have listed above.

At Vital Beats we make use of PostgreSQL, largely because it offers us a happy balance between good management and backup of data, and good standard command line tools, which is essential for us where we are deploying our solutions within Kubernetes / docker, and so more graphical tools are not always appropriate for us. PostgreSQL is also pretty universally supported in terms of language libraries and frameworks, without having to make compromises on how we want to store and layout our data.