It may be that you are not strong enough to do lift your own bodyweight yet. I've heard that exercises where your body moves through space are the best exercises, ie, squats, dips, chins etc.
Chins > pulldowns.
Dips > seated dip machine.
Pullups is basically identical to lat pulldowns (when using same grip), but pull ups will be more effective. Either exercise, you will still have "the feel of the iron griped in my hand"