Besides pull ups, i'm doing lat pulldown machine, nothing else, everything goes pretty good so far. I would recomend go for chin ups if you want to put bigger emphasis on biceps, while lats overload remain the same, compared to pull ups.
Chin ups is basically curls+pull ups in the same time, lul. Or you can do pull ups, they target your back overall and brachioradialis better, compared to chins. But remember that lats always get equally the same, grip doesn't matter for them.
I'm doing 10x6 weighted chin ups and lat pulldown 15x6 everyday.