A friend and I set some weight lifting goals for each other. One of the goals he set for me was for pullups/chinups because I'm not that great at them.

The goal is to do 4 sets of 10. Today I did 5 sets and the reps went like this: 10, 6, 4, 4, 2. taking about 1:30 rest between sets. I think longer rest would help increase the reps but I didn't have time for that today.

Would I be better off sticking to body weight or adding extra weight at some point. What would help me get to 4x10 faster?

I'm currently using a grip with palms facing each other because it feels best on my shoulders, the goal doesn't specify a grip or a rest period between sets.