Difficult to say which is most important . . .
Some of the more frequently used:
java.lang Used all the time. String may be the most frequently used class of alljavax.swingjava.awt.eventjava.utiljava.ioIn beginners' code, 99% of the API classes used will probably come from those packages.
Avoid packages whose names start with com.sun or similar; those classes might be changed in the future.
Don't go through packages reading all the classes, but look for the classes you think you might need and look at their API documentation.