My only word of caution to the OP and to tubbynewb stems from the way I see lots of guys doing pullups in the gym: with one or both shoulders hunching up toward their ears and staying there the whole time.
I don’t know exactly what’s going on in these cases, but it looks like their arms are overpowering their shoulders/backs. Whatever’s going on, it can’t be good.
When I started doing pullups again after a shoulder injury, I found some of the same happening to me – I felt like my shoulders (right – injured – one particularly) would slide up as I pulled down on the bar and that I couldn’t pull it back down.
I could still crank out 10 or 12 pullups after months away from doing them, but it was all arms: my back and shoulders were taken out of the picture after the first few reps. They felt horrible.
What I did to counter this: hang from the bar and just work on the “shoulder” portion of the pullup: the 3 or 4 inches at the bottom going from a dead hang (shoulders plugging your ears or close) to pulling your shoulder blades back and down, arms straight the whole time (feels like you’re sucking your arms into the shoulder sockets).
After a few weeks of doing this, I started adding in full ROM pullups (still from a dead hang) and they felt much better, like proper pullups again. (A proper pullup, to me, originates in the back – I like to think of pulling my elbows to my hips, though they never actually get there.)
Curl, bench, etc. all you want, just make sure you watch your form on pullups (and pulldowns) and that you don’t compensate for bad form/weak back with more arm work.
There have been several other threads on pullups if you care to look for them, and there are all sorts of strategies for doing your first/doing more.