I think either option has a lot of potential. In the late 80's COBOL was the thing that would get you a job. I learned JCL, COBOL and Easytrieve and worked as a programmer for a large bank. By the early 90's I had moved from programming to doing Operating System and network stuff. At that time network stuff consisted of things like VTAM and NCP for front end mainframe processors. Soon, TCP/IP came along and it was time to learn something new. Eventually I started fooling with Sun Unix and EMC storage and Sybase databases. By early 2000 time frame it was on to Windows Servers and Microsoft SQL server. I added Hitachi storage and Brocade switches to our systems and learned to do basic Storage Network administration. Eventually I became the go-to guy for the storage side of the operation.
The IT business changes all the time. Look in the paper in your area or search dice.com and monster. See what jobs are out there that interest you. Get some basic skills and take opportunities to do work on the side. I have learned VB programming doing side jobs. It helps me all the time at work. Get your foot in the door somewhere in I/T then do your best to expand your knowledge... you never know where it will take you, but if you work hard, are honest, fair, friendly, trustworthy and energetic, you could go far.
I agree that Oracle database administrators are paid well, I disagree with the statement about ignoring SQL Server. There are lots more SQL server jobs where I live than there are Oracle. An experienced SQL server admin/programmer can make a very good living.
I also agree that some programming skill is a must to be successful. If you go the database route, learn to write good sql. Find some guy that used to do Assembler and see how he writes SQL. You can learn a lot when you work with old farts, and the old fart may learn a lot from you.
Good luck!