Of course database. Easier to learn, and you can get testing jobs.
With core java, you can get development jobs.
But database shouldn't take one year and may not be enough. I learned it in one week.
I would say, first learn database, then learn core java. After that, you can combine two knowledge and use j2ee where you can use jdbc to access database from java.
If you want to go further, learn html, css and javascript, and combine that knowledge in j2ee using servlet and jsp with your java code.
After this, you are set for life, and this is certainly possible in one year, I learned these all in six weeks.