Many many people run Java Database code in Eclipse, and it works very well. There are many tutorials on the web.
If you would like help here you must explain exactly what you tried and what problems you had.
use javadb , it is already within the java sdk so there is no need for you to utilize a separate database.
i personally love to use netbeans.i used eclipse for many years before but there is one java project that i made where eclipse was not able to handle, it crashed many times and it is so slow.with netbeans, it is just nothing.it works perfectly, but it is just a preference, so there's a bias