Wow. Welcome to the world of databases!
Based on this posting, you are just the kind of person that we all like to help (well, maybe not blindman, but you'll get used to him anyway

). You seem to be the kind of person that makes good choices, actively wants to learn, and has a passion for databases. If that is the case, I think that you're in good company here!
I started out on a twin-brontosaurus system. We had two birds whose beaks chattered when they dropped into holes in stone cards. The printer had three squirrels with chisels cutting roman numerials into clay tablets that were pulled along by wooly mamoths. Think
The Flintstones. Naturally, you'll have to take a slightly different approach because it is so hard to find a brontosaurus these days!
While zOS DB2 and Oracle are still the "big dollar" shops, I wouldnt' recommend them as career builders for someone trying to get started. They tend to be very much controlled by an "old boys network" that makes it very hard to get in without some verifyable experience, and that experince is practically impossible to come by from small businesses and volunteer gigs.
For the environment that interests you, MySQL and Microsoft SQL Server are quite promising, and DB2 UDB is also a strong marginal contender (with a much stronger upgrade path to bigger dollar jobs once you get some experience). These gigs will certainly put food on the table and keep you warm and dry as you get the experience that you need to start the hunt for your first full time job as a DBA.
Keep in mind one of the fundamental truths about computers. It doesn't matter whether the topic of interest is hardware, operating systems, programming languages, databases, or anything else... The first one you learn is hard because it is the first.

The second one is hard because it isn't the first.

Once you get past the second one, the rest are all just "variations on a theme" and learning another one won't bother you much!
-PatP