Honestly, about 23 years ago I dove into LAMP (Linux/Apache/MySQL/PHP) and it was the best thing I could have ever done for myself, career-wise.
As one of those basket-weaving "Asian Studies" graduates with an unmarketable degree (but a pronounced underdeveloped skillset in electronics and computing) I taught myself relational database theory by accident while learning MySQL and PHP in order to build a mileage reimbursement database and program. Built the whole damn thing with bash, vi, and the mysql CLI. I turned it into a career where I'm in the top of my field in the Phoenix market, specializing in Microsoft SQL Server and performance oriented database design.
One doesn't have to go to such extremes though. MySQL is an open source database engine and it can be administered or accessed via Toad or PHPMyAdmin rather than its default CLI.
To that point, MS SQL Express Edition is a reasonably featured and free version of the latest version of Microsoft SQL Server. It can be administered with SQL Server Management Studio, which is a free download from Microsoft. It allows databases up to 10GB in size and up to 10 simultaneous connections before throttling itself and attempting to compel you to move to SQL Standard Edition.
There's really no point working with any RDBMS that doesn't have a dedicated processing engine. Access and Base are ugly tools, IMO.
There are dozens of people at my company that aren't former DBA's or software devs that know T-SQL. It's a very marketable skill. It has slight variations from Oracle to MySQL to MS-SQL, but the core language remains cross platform compatible for the most part. The hard part of learning databases isn't the T-SQL, it's the relational database theory and understanding normalization.