MongoDB actually is one of the fastest beasts on the market and it allows for hundreds of thousands inserts per second and it is also incredibly stable -- but, as with all technologies, it depends on the use case and how you use it.
If you need to store, let's say, documents or if you collect data from various sources in different formats and want to store that collected data in one central location, then a NoSQL database is a great choice. If you, on the other hand, simply need an address database with a fistful of normalized tables, than traditional SQL databases like MySQL probably make more sense.
Unfortunately, there is no simple advice for which one might be the right choice.
But there is an elephant in the room that people always pretend not to see: Licensing.
MySQL/Mariadb AND THEIR CONNECTORS(!) are licensed under the GPL. That's wonderful, isn't it? Because when you use those connectors, your own software MUST be put under the GPL as well. That's why they call it a VIRAL license. So: Your own software implicitly becomes open source software as well when you use the official connectors - unless, at least in case of MySQL, you purchase a commercial license from Oracle. There are no commercial Mariadb licenses, because Mariadb is a fork of MySQL and the company behind Mariadb does not own the rights to the original work (MySQL) anymore: Monty Widenius sold it all to Sun Microsystems when he sold his company MySQL AB for a billion dollars; he than later took the GPL code base and started his new company with it -- that tells you everything you need to know about basing a business on open source or "buying" a company that was built on open source.
SQLITE is in the public domain, so you actually can do it with whatever you want and use it in any way you seem fit without any obligations whatsoever. Apple uses it in a lot of its products, they even used it in the now discontinued software "Aperture" (which was a great product in my opinion, I loved it).
MonogDB uses a different breed of licenses, and the official "drivers" are licensed under the terms of the Apache 2.0 license, which is much more liberal and more permissive than the GPL.
