Zakir,
Go for
core Java first. No question about that.
Once your concepts in core java are crystal clear J2EE will make more sense.
Dont even think of going to J2EE untill core java fundamentals are rock solid.
At the end of the day your fundamental concepts will count.
Initially try to dig down into the core java code. Once you are confident in core java then only go for J2EE.
Get your core java concepts rock solid first
dont hurry to get into J2EE. Give maximum time to core Java.
Ofcourse you can try to go for J2EE but to be technically good it takes times and efforts. So first get your core java concepts very clear. It will surely help while doing J2EE!