That "lag" is latency, and it is not caused by the mic. No, you cannot plug the 'phones into the mic, what you need is an "interface" that has a headphone jack as well as the proper mic input, and you use THAT to record through and monitor from. I am guessing that you have a soundcard at this point? You need to replace that with a proper interface box.
And, while the Rode is a decent condenser for the bucks, condensers like that do not serve you well in a typical home environment that hasn't had accoustical treatments to it. It may very well pick up too much of the room and sound worse than a mic with a tighter pattern and less sensitivity, such as a Shure SM57/58. Just a thought, void of any advertising or marketing hype.

As the Moon said, changing the microphone won't affect the delay you hear in the headphones when you monitor through the computer. To avoid a delay, there needs to be a path in the interface hardware between the microphone input and the headphone output.

If you do go for the NT1-A bundle (which includes an M-Audio FastTrack interface), all you would need to do is push the button on the interface to activate the direct monitoring function. Easy.

The NT1-A is a very good mic for its price point, but, as the Moon mentioned, condenser mics like that do have disadvantages when recording in less-than-perfect acoustic environments. You could consider getting the NT1-A bundle and an SM58 dynamic mic as well. The 58 would be good for close-miked vocals, but the FastTrack is notoriously short of gain when using dynamic mics on things like acoustic guitars or on distant sources.

Thank you both very much for your replies.I have a better understanding now,an some food for thought..cheer's